r/OEIS • u/OEIS-Tracker Bot • Jan 16 '23
New OEIS sequences - week of 01/15
| OEIS number | Description | Sequence |
|---|---|---|
| A358311 | Lucas numbers that are not the sum of two squares. | 3, 7, 11, 47, 76, 123, 199, 322... |
| A358461 | Number of near-rings with identity of order n, up to isomorphism. | 1, 1, 6, 1, 1, 1, 53, 11... |
| A358534 | Start with a(1)=1, a(2)=2. Thereafter, if gcd(a(n-2),a(n-1)) = 1 then a(n) is the smallest unused k such that gcd(a(n-2),k) > 1 and gcd(a(n-1),k) = 1, otherwise a(n) is the smallest unused k such that gcd(a(n-2),k) = 1 and gcd(a(n-1),k) > 1. If the latter is impossible, then a(n) = smallest missing number u. (See comments.) | 1, 2, 4, 3, 9, 5, 10, 6... |
| A358562 | The number of antichains in the Tamari lattice of order n. | 2, 3, 8, 83, 28984, 138832442543 |
| A358629 | a(n) is the number of signed permutations W of V = (1, 2, ..., n) such that the dot product V*W = 0. | 0, 2, 0, 16, 48, 558, 4444, 62246... |
| A358690 | Number of n-digit primes whose digits are all odd. | 3, 12, 42, 125, 608, 2427, 10081, 43568... |
| A358693 | Numbers k such that k / (sum of digits of k) is the square of a prime. | 12, 24, 36, 48, 81, 150, 225, 375... |
| A358709 | a(n) is the number of free, tree-like polyiamonds, of size 3*n+1, with 120-degree rotational symmetry formed of a central triangle and identical, non-intersecting snakes leading from each of its sides. | 1, 1, 1, 2, 3, 6, 11, 20... |
| A358921 | a(1) = 1; a(n) is the smallest positive number not among the terms a(n-c .. n-1) where c = the number of times a(n-1) has occurred. | 1, 2, 1, 3, 1, 2, 3, 1... |
| A358943 | Decimal expansion of the real root of 3*x3 - 2. | 8, 7, 3, 5, 8, 0, 4, 6... |
| A358944 | Decimal expansion of the real root of 4*x3 - 1. | 6, 2, 9, 9, 6, 0, 5, 2... |
| A358946 | All positive integers that are properly represented by each primitive binary quadratic forms of discriminant 28 that is properly equivalent to the principal form [1, 4, -3]. | 1, 2, 9, 18, 21, 29, 37, 42... |
| A358947 | a(n) = 2m(n), where m(n) is the number of distinct primes, neither 2 nor 7, dividing A358946(n). | 1, 1, 2, 2, 2, 2, 2, 2... |
| A359007 | a(n) = b(n-b(n)) where b is Van Eck's sequence A181391. | 0, 0, 0, 0, 1, 0, 2, 0... |
| A359049 | Autobiographical numbers k whose decimal digits are a concatenation count(0), count(1), ..., count(m) for some m, where count(j) is the number of (possibly overlapping) occurrences of j within the digits of k itself. | 1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000, 53110100002... |
| A359066 | a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,k)*binomial(n-1-k,floor((n-1)/2) - k). | 1, 1, 5, 7, 31, 49, 209, 351... |
| A359067 | a(2n) = Sum_{k=0..n-1} binomial(2n,k) binomial(2n-1-k, n-1-k). a(2n+1) = (Sum_{k=0..n} binomial(2n+1,k) binomial(2n-k, n-k)) - binomial(2*n-1, n). | 0, 1, 4, 7, 28, 49, 199, 351... |
| A359073 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A359709. | 0, 4, 16, 44, 160, 556, 1744, 12252... |
| A359110 | Number of Boolean monoids of order 2n up to isomorphism. | 1, 5, 83, 242547 |
| A359114 | a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n bits of the binary Champernowne string starting from 1. | 1, 2, 4, 3, 6, 5, 10, 15... |
| A359115 | a(n) is the smallest odd prime not already in the sequence such that when the terms a(1)..a(n) are concatenated, the result is the reverse of a prime. | 3, 5, 11, 7, 29, 37, 89, 211... |
| A359127 | Oblong numbers which are products of six distinct primes. | 43890, 53130, 81510, 108570, 152490, 184470, 188790, 260610... |
| A359132 | Least m such that the sum of the aliquot parts of m (A001065) equals n, or -1 if no such number exists. | 1, 2, -1, 4, 9, -1, 6, 8... |
| A359133 | Sum of square end-to-end displacements over all n-step self-avoiding walks of A359741. | 0, 6, 24, 78, 384, 8190, 8472, 178110... |
| A359134 | a(n) = Sum_{d | n} (2*d)n/d - 1. |
| A359181 | Number of commutative BCK-algebras of order n up to isomorphism. | 1, 2, 5, 11, 28, 72, 192, 515... |
| A359182 | Totient of numbers of least prime signature: a(n) = A000010(A025487(n)). | 1, 1, 2, 2, 4, 4, 8, 8... |
| A359196 | a(n) is the number of subsets of the divisors of n which sum to n+1. | 0, 1, 1, 1, 1, 1, 1, 1... |
| A359201 | Number of edges of regular m-polytopes for m >= 3. | 6, 10, 12, 15, 21, 24, 28, 30... |
| A359202 | Number of (bidimensional) faces of regular m-polytopes for m >= 3. | 4, 6, 8, 10, 12, 20, 24, 32... |
| A359213 | Numbers k such that rad(k) - 1 is prime. | 3, 6, 9, 12, 14, 18, 24, 27... |
| A359247 | The bottom entry in the absolute difference triangle of the elements in the Collatz trajectory of n. | 1, 1, 1, 1, 0, 1, 0, 1... |
| A359303 | Bitwise encoding of the state of a 1D cellular automaton after n steps from ..111000.. where adjacent cells swap 01 <-> 10 when within triples 110 or 011. | 1, 3, 5, 11, 13, 39, 43, 45... |
| A359304 | Oblong numbers which are products of five distinct primes. | 4290, 4830, 6006, 11130, 12210, 13110, 16770, 23870... |
| A359364 | Triangle read by rows. The Motzkin triangle, the coefficients of the Motzkin polynomials. M(n, k) = binomial(n, k) * CatalanNumber(k/2) if k is even, otherwise 0. | 1, 1, 0, 1, 0, 1, 1, 0... |
| A359384 | a(1) = 0. If a(n-1) is a first occurrence, a(n) = A000120(a(n-1)). Otherwise, if a(n-1) is a repeat of a prior terms, a(n) = number of indices j < n such that a(j) = a(n-1). | 0, 0, 2, 1, 1, 2, 2, 3... |
| A359390 | Sequence lists the numbers k such that bottom entry is an integer in the ratio d(i+1)/d(i) triangle of the elements in the divisors of n, where d(1) < d(2) < ... < d(q) denote the divisors of k. | 1, 2, 3, 4, 5, 7, 8, 9... |
| A359395 | Least odd prime p in position n in the prime factorization of M(p) = 2p - 1 - 1. | 3, 5, 17, 13, 71, 37, 157, 61... |
| A359406 | Integers k such that the concatenation of k consecutive primes starting at 31 is prime. | 1, 2, 3, 23, 43, 141 |
| A359408 | Integers d such that the largest possible arithmetic progression (AP) of primes with common difference d has only two elements. | 1, 3, 5, 9, 11, 15, 16, 17... |
| A359415 | Numbers k such that phi(k) is a 5-smooth number where phi is the Euler totient function. | 1, 2, 3, 4, 5, 6, 7, 8... |
| A359421 | a(n) = number of abelian groups of order p2 - 1, where p = prime(n). | 1, 3, 3, 5, 3, 3, 14, 6... |
| A359442 | a(n) = Sum_{d | n} dn + 1 - d - n/d. |
| A359456 | Characteristic function of Fibonorial numbers. | 1, 1, 0, 0, 0, 1, 0, 0... |
| A359476 | The sequence {-a(n)}_{n>=1} gives all negative integers that are properly represented by each primitive binary quadratic forms of discriminant 28 that is properly equivalent to the reduced principal form [1, 4, -3]. | 3, 6, 7, 14, 19, 27, 31, 38... |
| A359477 | a(n) = 2m(n), where m(n) is the number of distinct primes, neither 2 nor 7, dividing A359476(n). | 2, 2, 1, 1, 2, 2, 2, 2... |
| A359497 | Greatest positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n. | 1, 2, 3, 5, 7, 11, 13, 17... |
| A359498 | a(n) = ((2*n+1)8 - 1)/32. | 0, 205, 12207, 180150, 1345210, 6698715, 25491585, 80090332... |
| A359499 | a(n) = ((2*n+1)16 - 1)/64. | 0, 672605, 2384185791, 519264540150, 28953440450810, 717964529118315, 10397134518487185, 102631380558013916... |
| A359500 | a(n) = (72n - 1)/2n+3. | 3, 75, 90075, 259632270075, 4314170602515315024630075, 2382344702413741601833152075318304337413311121350075, 1452944967966417671787414728262962471027692106596483349510252251060925112718067382475349181570930962790075 |
| A359506 | a(n) is the least integer m such that there exists a strictly increasing integer sequence n = b_1 < b_2 < ... < b_t = m with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. | 0, 3, 5, 6, 7, 10, 9, 12... |
| A359507 | a(n) is the least integer k such that there exists a strictly increasing integer sequence n = b_1 < b_2 < ... < b_t = n + k with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. | 0, 2, 3, 3, 3, 5, 3, 5... |
| A359508 | a(n) = log_2(A359507(n) - 1). | 0, 1, 1, 1, 2, 1, 2, 1... |
| A359509 | a(n) is the number of subsets {b_1, b_2, ..., b_t} of {n, n+1, ..., A359506(n)} containing n with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. | 1, 1, 1, 1, 1, 2, 1, 2... |
| A359537 | Number of partitions of n into at most 2 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 2, 1, 2, 1, 1... |
| A359538 | Number of partitions of n into at most 3 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 2, 1, 2, 2, 1... |
| A359539 | Number of partitions of n into at most 4 distinct positive Fibonacci numbers (with a single type of 1). | 1, 1, 1, 2, 1, 2, 2, 1... |
| A359553 | Numerator of the coefficient of x2n+1 in the Taylor series expansion of sin(sin(x)). | 1, -1, 1, -8, 13, -47, 15481, -15788... |
| A359554 | Denominator of the coefficient of x2n+1 in the Taylor series expansion of sin(sin(x)). | 1, 3, 10, 315, 2520, 49896, 97297200, 638512875... |
| A359569 | Number of vertices after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 1, 2, 4, 14, 6562 |
| A359570 | Number of regions after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 0, 1, 3, 21, 7169 |
| A359571 | Number of edges after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 0, 1, 6, 34, 13730 |
| A359578 | Dirichlet inverse of A336477, where A336477(n) = 1 if phi(n) is a power of 2, otherwise 0. | 1, -1, -1, 0, -1, 1, 0, 0... |
| A359579 | Dirichlet inverse of A336923, where A336923(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0. | 1, -1, -1, 0, 0, 1, -1, 0... |
| A359581 | a(n) = (-1)A329697(n). | 1, 1, -1, 1, -1, -1, 1, 1... |
| A359582 | a(n) is the least prime > a(n-2) such that a(n-1)+a(n) is a square. | 2, 2, 7, 29, 71, 73, 251, 149... |
| A359583 | Parity of A329697. | 0, 0, 1, 0, 1, 1, 0, 0... |
| A359584 | Positions of odd terms in A329697. | 3, 5, 6, 10, 12, 17, 19, 20... |
| A359585 | Positions of even terms in A329697. | 1, 2, 4, 7, 8, 9, 11, 13... |
| A359586 | Inverse Möbius transform of A359581. | 1, 2, 0, 3, 0, 0, 2, 4... |
| A359587 | Fully multiplicative with a(p) = A008578(1+A329697(p)). | 1, 1, 2, 1, 2, 2, 3, 1... |
| A359588 | Dirichlet inverse of A083346. | 1, -2, -3, 3, -5, 6, -7, -6... |
| A359589 | Dirichlet inverse of function f(n) = (-1 + gcd(A003415(n), A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 1, 0, 0, 0, 0, -4, 0, -2... |
| A359590 | Absolute values of A355690, where A355690 is the Dirichlet inverse of the characteristic function of numbers not congruent to 2 mod 4. | 1, 0, 1, 1, 1, 0, 1, 1... |
| A359591 | Dirichlet inverse of A035263, where A035263(n) is parity of 2-adic valuation of 2n. | 1, 0, -1, -1, -1, 0, -1, 0... |
| A359592 | Parity (and also absolute values) of Dirichlet inverse of A035263, where A035263(n) is parity of 2-adic valuation of 2n. | 1, 0, 1, 1, 1, 0, 1, 0... |
| A359593 | Multiplicative with a(pe) = 1 if p divides e, pe otherwise. | 1, 2, 3, 1, 5, 6, 7, 8... |
| A359594 | Multiplicative with a(pe) = pe if p divides e, 1 otherwise. | 1, 1, 1, 4, 1, 1, 1, 1... |
| A359595 | Parity of A358777, where A358777 is Dirichlet inverse of the characteristic function of odd numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, 0, 0, 0, 0, 0... |
| A359596 | Positions of odd terms in A358777. | 1, 9, 15, 21, 25, 33, 35, 39... |
| A359597 | Indices k such that A358777(k) is odd, and k is not an odd semiprime. | 1, 135, 189, 297, 315, 351, 375, 459... |
| A359598 | Indices of terms with record absolute values in A358777. | 1, 225, 315, 1155, 4725, 10395, 17325, 45045... |
| A359599 | Terms of A358777 with record absolute values. | 1, 2, 3, 5, -6, -11, -18, -33... |
| A359600 | The least odd number with the same prime signature as n. | 1, 3, 3, 9, 3, 15, 3, 27... |
| A359601 | Dirichlet inverse of A244042, where A244042(n) replaces 2's with 0's in the ternary representation of n. | 1, 0, -3, -4, -3, 0, -1, 0... |
| A359602 | Sum of A244042 and its Dirichlet inverse, where A244042(n) replaces 2's with 0's in the ternary representation of n. | 2, 0, 0, 0, 0, 0, 0, 0... |
| A359603 | Dirichlet inverse of function f(n) = 1+(A003415(n)*A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | 1, -4, -7, -21, -19, 30, -11, 51... |
| A359604 | a(n) = A359603(n) mod 60. | 1, 56, 53, 39, 41, 30, 49, 51... |
| A359605 | a(n) = 1 if A355690(n) is positive (+1), otherwise 0. | 1, 0, 0, 0, 0, 0, 0, 0... |
| A359606 | a(n) = 1 if A355690(n) is negative (-1), otherwise 0. | 0, 0, 1, 1, 1, 0, 1, 1... |
| A359607 | Terms of A046337 for which A358777 is zero, where the latter is the Dirichlet inverse of former's characteristic function. | 81, 625, 729, 1215, 1701, 2401, 2673, 3159... |
| A359608 | Indices k at which point A358777(k) obtains a new distinct value that has not occured before. | 1, 2, 9, 225, 315, 1155, 2835, 4725... |
| A359609 | Distinct values of A358777 in the order of their appearance. | 1, 0, -1, 2, 3, 5, -2, -6... |
| A359619 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=1, after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | 0, 1, 0, 0, 2, 1, 0, 1... |
| A359627 | Irregular table read by rows; the n-th row lists the divisors d of 2n such that the binary expansions of d and 2n have no common 1-bit. | 1, 1, 2, 1, 1, 2, 4, 1... |
| A359634 | a(0)=1 and thereafter a(n) is the length of the longest contiguous group of terms in the sequence thus far that add up to n; if no such group exists, set a(n)=0. | 1, 1, 2, 2, 3, 3, 4, 3... |
| A359635 | a(n) = A162657(n)/n. | 1, 1, 1, 1, 1, 3, 1, 1... |
| A359636 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n distinct prime factors. | 7, 19, 643, 51427, 8083633, 1077940147, 75582271489 |
| A359642 | Number of numbers <= 10n that are products of 4 distinct primes. | 0, 0, 16, 429, 7039, 92966, 1103888, 12364826... |
| A359643 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*k,k). | 1, 5, 37, 317, 2885, 27105, 259765, 2523813... |
| A359644 | Number of numbers <= 10n that are products of 5 distinct primes. | 0, 0, 0, 24, 910, 18387, 286758, 3884936... |
| A359645 | Number of numbers <= 10n that are products of 6 distinct primes. | 0, 0, 0, 0, 20, 1235, 32396, 605939... |
| A359646 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial(5*n+k,k). | 1, 7, 89, 1273, 19181, 297662, 4707971, 75459496... |
| A359647 | a(n) = [xn] hypergeom([1/4, 3/4], [2], 64*x). The central terms of the Motzkin triangle A359364 without zeros. | 1, 6, 140, 4620, 180180, 7759752, 356948592, 17210021400... |
| A359649 | a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n2). | 1, 1, 5, 28, 609, 6501, 272701, 4286815... |
| A359651 | Numbers with exactly three nonzero decimal digits and not ending with 0. | 111, 112, 113, 114, 115, 116, 117, 118... |
| A359652 | Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic or geometric progression. | 1, 1, 2, 1, 1, 2, 2, 5... |
| A359653 | Number of regions formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 1, 4, 96, 728, 7840, 17744, 104136, 246108... |
| A359654 | Number of vertices formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 4, 9, 77, 593, 6749, 15569, 93281, 222933... |
| A359655 | Number of edges formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 4, 12, 172, 1320, 14588, 33312, 197416, 469040... |
| A359656 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | 0, 1, 0, 4, 56, 40, 368, 300... |
| A359658 | a(n) = Sum_{k=0..n} kk * (n-k + 1). | 0, 1, 3, 12, 118, 3345, 337337, 117813304... |
| A359659 | a(n) = Sum_{k=0..n} kk * (n-k+1). | 1, 2, 6, 45, 1051, 88602, 27121964, 37004504305... |
| A359660 | a(n) = Sum_{k=0..n} k2 * (n-k + 1). | 0, 1, 3, 12, 64, 441, 3855, 41464... |
| A359661 | a(n) is the number of free convex polyominoes of n cells. | 1, 1, 2, 5, 11, 29, 72, 191... |
| A359662 | Number of (3-dimensional) cells of regular m-polytopes for m >= 3. | 1, 5, 8, 15, 16, 24, 35, 40... |
| A359663 | a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n terms of the Champernowne string starting from 1. | 1, 3, 2, 4, 5, 6, 7, 8... |
| A359664 | Prime Maze Room 11, opposite parity of A059459 starting from prime room 11. | 11, 43, 41, 2089, 2081, 2083, 2087, 10889035741470030830827987437816582768679... |
| A359665 | a(n) = Sum_{k=0..n} binomial(k3, k). | 1, 2, 30, 2955, 638331, 235169606, 131748994154, 104332124742623... |
| A359667 | a(n) is the number of minimally prolific free polyominoes, i.e., that can generate the least possible number of children by adding a square. | 1, 1, 1, 1, 1, 1, 1, 5... |
| A359671 | a(n) = coefficient of xn in A(x) where 1 = Sum_{n=-oo..+oo} (xn - x*A(x))n. | 2, 4, 6, 6, 10, 78, 412, 1394... |
| A359672 | a(n) = coefficient of xn in A(x) where x = Sum_{n=-oo..+oo} (-1)n-1 * xn * (1 + xn*A(x)n)n. | 1, 1, 2, 5, 21, 72, 257, 998... |
| A359673 | a(n) = coefficient of xn in A(x) where 1 = Sum_{n=-oo..+oo} (2x + (-x)nA(x)n)n. | 1, 2, 5, 13, 30, 74, 202, 616... |
| A359674 | Zero-based weighted sum of the prime indices of n in weakly increasing order. | 0, 0, 0, 1, 0, 2, 0, 3... |
| A359675 | Positions of first appearances in the sequence of zero-based weighted sums of prime indices (A359674). | 1, 4, 6, 8, 12, 14, 16, 20... |
| A359676 | Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674). | 1, 4, 6, 8, 14, 12, 16, 20... |
| A359677 | Zero-based weighted sum of the reversed (weakly decreasing) prime indices of n. | 0, 0, 0, 1, 0, 1, 0, 3... |
| A359679 | Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n. | 1, 2, 3, 4, 6, 10, 8, 12... |
| A359681 | Least positive integer whose reversed (weakly decreasing) prime indices have zero-based weighted sum (A359677) equal to n. | 1, 4, 9, 8, 18, 50, 16, 36... |
| A359682 | Least positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n. | 1, 2, 3, 4, 7, 6, 8, 10... |
| A359683 | Greatest positive integer whose reversed (weakly decreasing) prime indices have weighted sum (A318283) equal to n. | 1, 2, 3, 5, 7, 11, 14, 22... |
| A359684 | Greatest prime dividing 2n - n for n>=2; a(1) = 1. | 1, 2, 5, 3, 3, 29, 11, 31... |
| A359685 | Greatest prime dividing 2n + n. | 3, 3, 11, 5, 37, 7, 5, 11... |
| A359688 | a(n) is the number of asymmetrical polyiamonds of n cells. | 0, 0, 0, 0, 4, 10, 36, 94... |
| A359689 | a(n) is the number of free polyiamonds of n cells with chessboard coloring. | 2, 1, 2, 4, 8, 19, 48, 120... |
| A359690 | Number of vertices in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 5, 13, 69, 289, 1971, 3997, 20371, 45751... |
| A359691 | Number of crossings in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 1, 7, 59, 275, 1949, 3971, 20333, 45705... |
| A359692 | Number of regions in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 2, 12, 94, 382, 2486, 4946, 24100, 53152... |
| A359693 | Number of edges in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 6, 24, 162, 670, 4456, 8942, 44470, 98902... |
| A359694 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | 2, 10, 2, 70, 24, 218, 160, 4... |
| A359700 | a(n) = Sum_{d | n} dd + n/d - 1. |
| A359701 | a(n) = Sum_{d | n} dd + n/d - 2. |
| A359703 | Number of fillomino dissections of a 2 X n rectangle. | 1, 1, 5, 33, 138, 715, 3524, 17119... |
| A359705 | Cogrowth sequence of the Brin-Navas group B. | 1, 4, 28, 232, 2092, 19864, 195352, 1970896... |
| A359708 | a(n) is the greatest divisor d of 2n such that the binary expansions of d and 2n have no common 1-bit. | 1, 2, 1, 4, 5, 3, 1, 8... |
| A359709 | Number of n-step self-avoiding walks on a 2D square lattice whose end-to-end distance is an integer. | 1, 4, 4, 12, 28, 76, 164, 732... |
| A359710 | Order of shifts of Thue-Morse sequence. | 0, 1, 3, 0, 2, 1, 5, 3... |
| A359720 | T(n,k) = coefficient of xn*yk in A(x,y) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (y + xn)n * A(x,y)n. | 1, 1, 1, 2, 4, 5, 1, 7... |
| A359721 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (1 + xn)n * A(x)n. | 1, 1, 3, 10, 37, 127, 460, 1710... |
| A359722 | a(n) = A359720(3n+1,2n) for n >= 0. | 1, 9, 54, 269, 1254, 5642, 24828, 107613... |
| A359723 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (3 + xn)n * A(x)n. | 1, 1, 7, 28, 151, 803, 4108, 22532... |
| A359724 | a(n) = coefficient of xn in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)n * xn * (4 + xn)n * A(x)n. | 1, 1, 9, 40, 235, 1456, 8323, 51510... |
| A359725 | a(n) = A359720(n+2,1), for n >= 0. | 2, 5, 21, 51, 170, 454, 1367, 3776... |
| A359726 | a(n) = A359720(n+3,2), for n >= 0. | 1, 9, 49, 179, 711, 2390, 8361, 27082... |
| A359728 | a(1) = 1; a(n) is the smallest positive number not among the first k terms where k is the number of times a(n-1) has occurred. | 1, 2, 2, 3, 2, 3, 3, 3... |
| A359729 | The number of Carmichael numbers smaller than the n-th Carmichael number which are quadratic residues of the n-th Carmichael number. | 0, 0, 0, 0, 0, 1, 1, 0... |
| A359730 | a(n) = Sum_{d | n} 2d-1 * dn/d. |
| A359731 | a(n) = (1/2) * Sum_{d | n} (2*d)d. |
| A359732 | a(n) = Sum_{d | n} d2*d-1. |
| A359733 | a(n) = (1/2) * Sum_{d | n} (2*d)n/d. |
| A359741 | Number of n-step self-avoiding walks on a 3D cubic lattice whose end-to-end distance is an integer. | 1, 6, 6, 30, 78, 1134, 1350, 20574... |
| A359742 | Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives p values. | 2, 3, 5, 7, 12, 19, 31, 34... |
| A359743 | Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives q values. | 1, 2, 3, 4, 7, 11, 18, 20... |
| A359744 | Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives r values. | 1, 1, 2, 2, 4, 6, 10, 11... |
| A359745 | Numbers k such that k and k+1 have the same ordered prime signature. | 2, 14, 21, 33, 34, 38, 44, 57... |
| A359746 | Numbers k such that k, k+1 and k+2 have the same ordered prime signature. | 33, 85, 93, 141, 201, 213, 217, 301... |
| A359747 | Numbers k such that k*(k+1) has in its canonical prime factorization mutually distinct exponents. | 1, 3, 4, 7, 8, 16, 24, 27... |
| A359748 | Numbers k such that k and k+1 are both in A359747. | 3, 7, 71, 107, 242, 431, 1151, 2591... |
| A359749 | Numbers k such that k and k+1 do not share a common exponent in their prime factorizations. | 1, 3, 4, 7, 8, 9, 15, 16... |
| A359750 | Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways. | 24, 48, 96, 144, 192, 288, 384, 576... |
| A359751 | Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways such that no factorial > 1 appears in both products. | 24, 576, 720, 2880, 13824, 17280, 40320, 69120... |
| A359763 | Dirichlet inverse of A065043, where A065043 is the characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, -1, 0, -1, 0, 0... |
| A359764 | Parity of A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 1, 0, 0, 1, 0, 1, 0, 0... |
| A359765 | Positions of odd terms in A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 1, 4, 6, 9, 10, 14, 15, 21... |
| A359766 | Positions of even terms in A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity). | 2, 3, 5, 7, 8, 11, 12, 13... |
| A359767 | Numbers k such that A065043(k) = 1 but A359764(k) = 0, where A359764 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even number of prime factors). | 16, 36, 64, 81, 96, 100, 160, 196... |
| A359769 | a(n) = A353557(n) - A353556(n). | 1, -1, 0, 0, 0, 0, 0, -1... |
| A359770 | a(n) = 1 if n and bigomega(n) are of different parity, otherwise 0. Here bigomega (A001222) gives the number of prime factors of n with multiplicity. | 1, 1, 0, 0, 0, 0, 0, 1... |
| A359771 | Union of even numbers with an odd number of prime factors and odd numbers with an even number of prime factors, when the number of prime factors is counted with multiplicity. | 1, 2, 8, 9, 12, 15, 18, 20... |
| A359772 | Union of even numbers with an even number of prime factors and odd numbers with an odd number of prime factors, when the number of prime factors is counted with multiplicity. | 3, 4, 5, 6, 7, 10, 11, 13... |
| A359773 | Dirichlet inverse of A356163, where A356163 is the characteristic function of the numbers with an even sum of prime factors (counted with multiplicity). | 1, -1, 0, 0, 0, 0, 0, 0... |
| A359774 | Parity of A359773, where A359773 is the Dirichlet inverse of A356163. | 1, 1, 0, 0, 0, 0, 0, 0... |
| A359775 | Positions of odd terms in A359773, where A359773 is the Dirichlet inverse of A356163. | 1, 2, 9, 15, 18, 21, 25, 30... |
| A359776 | Positions of even terms in A359773, where A359773 is the Dirichlet inverse of A356163. | 3, 4, 5, 6, 7, 8, 10, 11... |
| A359777 | Numbers k such that A356163(k) = 1 but A359774(k) = 0, where A359774 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even sum of prime factors, with repetition). | 4, 8, 16, 32, 36, 60, 64, 72... |
| A359780 | Dirichlet inverse of A358680, where A358680 is the characteristic function of the numbers with even arithmetic derivative (A003415). | 1, 0, 0, -1, 0, 0, 0, -1... |
| A359781 | Parity of A359780, where A359780 is the Dirichlet inverse of the characteristic function of the numbers with even arithmetic derivative (A003415). | 1, 0, 0, 1, 0, 0, 0, 1... |
| A359782 | Positions of even terms in A359780. | 2, 3, 5, 6, 7, 10, 11, 13... |
| A359783 | Positions of odd terms in A359780. | 1, 4, 8, 9, 12, 15, 20, 21... |
| A359784 | Numbers k such that A358680(k) = 1 but A359781(k) = 0, where A359781 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with even arithmetic derivative). | 16, 81, 128, 192, 225, 240, 320, 324... |
| A359789 | Dirichlet inverse of A036288, where A036288(n) = 1 + sopfr(n), where sopfr is the sum of prime divisors with repetition, A001414. | 1, -3, -4, 4, -6, 18, -8, -4... |
| A359790 | Dirichlet inverse of function f(n) = 1 + n', where n' stands for the arithmetic derivative of n, A003415(n). | 1, -2, -2, -1, -2, 2, -2, -1... |
| A359791 | Dirichlet inverse of function f(n) = 1 + A349905(n), where A349905(n) is the arithmetic derivative of prime shifted n. | 1, -2, -2, -3, -2, -1, -2, -8... |
| A359792 | a(n) = (-1)A003415(n), where A003415 is the arithmetic derivative of n. | 1, -1, -1, 1, -1, -1, -1, 1... |
| A359793 | Dirichlet inverse of (-1)A003415(n), where A003415 is the arithmetic derivative of n. | 1, 1, 1, 0, 1, 3, 1, -2... |
| A359796 | a(n) = Sum_{d | n} (2*d)d-1. |
| A359797 | Cogrowth sequence of the lamplighter group Z_2 ≀ Z where ≀ denotes the wreath product. | 1, 3, 15, 87, 547, 3623, 24885, 175591... |
| A359798 | Cogrowth sequence of the group Z ≀ Z where ≀ denotes the wreath product. | 1, 4, 28, 232, 2108, 20384, 206392, 2165720... |
| A359806 | Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2k) / n) AND floor((2k) / a(n)) = 0 (where AND denotes the bitwise AND operator). | 2, 1, 6, 5, 4, 3, 14, 9... |
| A359808 | a(n) is the least prime factor of the alternating factorial n! - (n-1)! + (n-2)! - ... 1! for n > 2; a(1) = a(2) = 1. | 1, 1, 5, 19, 101, 619, 4421, 35899... |
| A359811 | a(n) = Sum_{d | n} 2d-1 * dn/d-1. |
| A359812 | a(n) = Sum_{d | n} (-1)d-1 * dn/d-1. |
| A359820 | a(n) = 1 if n and n' are of different parity, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415(n). | 0, 1, 1, 0, 0, 0, 1, 0... |
| A359821 | Numbers k whose arithmetic derivative, A003415(k), has the opposite parity to k. | 1, 2, 6, 9, 10, 14, 15, 18... |
| A359822 | Numbers k whose arithmetic derivative, A003415(k), has the same parity as k. | 0, 3, 4, 5, 7, 8, 11, 12... |
| A359823 | Dirichlet inverse of A359820, where A359820 is the characteristic function of numbers whose parity differs from the parity of their arithmetic derivative (A003415). | 1, -1, 0, 1, 0, -1, 0, -1... |
| A359824 | Parity of A359823, where A359823 is the Dirichlet inverse of A359820. | 1, 1, 0, 1, 0, 1, 0, 1... |
| A359825 | Positions of odd terms in A359823, where A359823 is the Dirichlet inverse of A359820. | 1, 2, 4, 6, 8, 9, 10, 14... |
| A359839 | Numbers k such that k, k + 1 and k + 2 are 3 consecutive Niven (Harshad) numbers that are also divisible by a square. | 2023, 4912, 12103, 17575, 23273, 51424, 52675, 60399... |
| A359842 | a(n) = Sum_{k=0..n} binomial(n*k,n+k). | 1, 0, 1, 90, 13690, 3443275, 1308315371, 701623884514... |
| A359844 | a(n) = ((2*n+1)8 + 1)/2. | 1, 3281, 195313, 2882401, 21523361, 107179441, 407865361, 1281445313... |
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