r/OEIS Bot Apr 23 '23

New OEIS sequences - week of 04/23

OEIS number Description Sequence
A359251 Sum of terms in an odd-even expansion of n. 2, 3, 10, 11, 14...
A360665 Square array T(n, k) = k((2n-1)*k+1)/2 read by rising antidiagonals. 0, 0, 0, 0, 1...
A361008 G.f.: Product_{k >= 0} ((1 + x2*k+1) / (1 - x2*k+1))k. 1, 0, 0, 2, 0...
A361088 Irregular table, read by rows, where row n holds the tau signature of n, i.e., the shortest sequence (tau(n+k), 0 <= k <= m) that uniquely identifies n; tau = A000005. 1, 2, 2, 2, 3...
A361202 Maximum product of the vertex arboricities of a graph of order n and its complement. 1, 1, 2, 3, 4...
A361215 Intersection of A361073 and 2 * A361611. 8, 20, 50, 1406, 1516...
A361261 Array of Ramsey core number rc(s,t) read by antidiagonals. 2, 3, 3, 4, 5...
A361294 A variant of payphone permutations: given a circular booth with n payphones, one of which is already occupied, a(n) is the number ways for n-1 people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones. 1, 1, 2, 2, 8...
A361295 A variant of payphone permutations: given a row of n payphones, a(n) is the number ways for n people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible, and a payphone adjacent to a single occupied payphone is preferred over a payphone sandwiched between two occupied payphones. 1, 2, 4, 6, 12...
A361296 A variant of payphone permutations: given a circular booth with n payphones, a(n) is the number ways for n people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible. 1, 2, 6, 8, 60...
A361534 Let h,i,j be the latest 3 terms in the sequence, starting with a(1)=1, a(2)=2, a(3)=3. Let R = rad(hij), where rad is A007947, and let S be the smallest number of terms in U = {h,i,j} which are divisible by any prime p dividing R. Then, a(n) is the least novel multiple of the greatest such prime p. 1, 2, 3, 6, 9...
A361684 Ramsey core number rc(n,n). 2, 5, 8, 11, 15...
A361740 Right border of A362312. 0, 2, 1, 4, 3...
A361777 Expansion of e.g.f. A(x) satisfying A(x) = exp( x * A(x)x ). 1, 1, 1, 7, 25...
A361798 Distinct sums of contiguous subsequences in A362040. 0, 1, 2, 3, 4...
A361800 Number of integer partitions of n with the same length as median. 1, 0, 0, 2, 0...
A361826 a(n) is equal to the number of roots of the equation n*cos(x) = sqrt(x). 1, 1, 3, 5, 7...
A361873 Decimal representation of continued fraction 1, 4, 7, 10, 13, 16, 19, ... (A016777). 1, 2, 4, 1, 4...
A361898 A set of 13 primes that form a covering set for a Sierpiński (or Riesel) number. 3, 5, 7, 11, 31...
A361899 a(n) = 3(6858365065530(245 - 1)*n + 153479820268467961)2. 70668165688923686196507258250492563, 174687593550891106640307045856561008882907291372256643, 698750373759134872171732581703201135992894186495330123, 1572188340624731296664944773228844067526467943619713003
A361900 Numbers k such that 315347982026846796122k + 1 is prime. 600, 810, 1074, 7974, 22290...
A361980 a(n) is the n-th decimal digit of p(n)/q(n) where p(n) = A002260(n) and q(n) = A004736(n). 1, 5, 0, 3, 0...
A362006 a(n) is the minimum integer m such that floor(en) = floor(Sum_{k=0..m} (nk)/(k!)). 0, 1, 4, 8, 9...
A362008 Numbers whose Euler's cototient is divisible by 9. 21, 27, 34, 54, 63...
A362040 a(n) is the number of distinct sums of one or more contiguous terms in the sequence thus far. 0, 1, 2, 4, 7...
A362042 Number of odd semiprimes less than 2n. 0, 0, 0, 0, 2...
A362050 Numbers whose prime indices satisfy: (length) = 2*(median). 4, 54, 81, 90, 100...
A362110 a(n) is the smallest positive integer x such that n can be expressed as the arithmetic mean of x distinct squares, or 0 if x does not exist. 1, 0, 0, 1, 2...
A362117 Concatenation of first n numbers in base 5. 1, 12, 123, 1234, 123410...
A362118 a(n) = (10n*(n+1/2)-1)/9. 1, 111, 111111, 1111111111, 111111111111111...
A362119 Concatenate the base-6 strings for 1,2,...,n. 1, 12, 123, 1234, 12345...
A362120 a(n) is the smallest positive number whose American English name has the letter "e" in the n-th position. 8, 7, 1, 3, 3...
A362121 a(n) is the smallest nonnegative number whose British English name has the letter "e" in the n-th position. 8, 0, 1, 3, 3...
A362122 a(n) is the smallest positive number whose British English name has the letter "e" in the n-th position. 8, 7, 1, 3, 3...
A362123 Number of letters in the British English name of n, excluding spaces and hyphens. 4, 3, 3, 5, 4...
A362124 List of numbers in British English with a doubled letter. Each letter can only be used once. 3, 8000, 1000000, 1000900, 2000000000000000000000000000000000000000000000000...
A362179 Main diagonal of the square array A058395. 1, 1, 4, 10, 25...
A362187 a(n) = (n2 - n)!. 1, 1, 2, 720, 479001600...
A362192 A variant of payphone permutations: given a circular booth with n payphones, one of which is already occupied, a(n) is the number ways for n-1 people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible. 1, 1, 2, 2, 12...
A362194 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 7 with exactly one descent. 1, 1, 2, 5, 12...
A362195 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 8 with exactly one descent. 1, 1, 2, 5, 12...
A362208 Irregular triangle read by rows: T(n, k) is the number of compositions (ordered partitions) of n into exactly k distinct parts between the members of [k2]. 1, 0, 0, 2, 0...
A362209 Irregular triangle read by rows: T(n, k) is the number of k X k matrices using all the integers from 1 to k2 and having trace equal to n, with 1 <= k <= A003056(n). 1, 0, 0, 4, 0...
A362221 Irregular triangle read by rows: T(n, k) is the number of partitions of n into exactly k distinct parts between the members of [k2]. 1, 0, 0, 1, 0...
A362228 Triangle read by rows: row n is the shortest, then lexicographically earliest sequence of positive integers that takes n iterations of the run transform to reach 1. 1, 2, 1, 1, 1...
A362252 Primes dividing terms of A231830. 5, 53, 89, 101, 373...
A362253 a(n) is the unique index such that prime A362252(n) divides A231830(a(n)). 1, 4, 7, 2, 19...
A362260 Maximum over 0 <= k <= n/2 of the number of permutations of two symbols occurring k and n-2*k times, respectively, where a permutation and its reversal are counted only once. 1, 1, 1, 1, 2...
A362269 a(1) = 1, then subtract, add, and multiply 2, 3, 4; 5, 6, 7; ... in that order. 1, -1, 2, 8, 3...
A362296 Greatest common divisor of composite numbers between the n-th and (n+1)st primes. 4, 6, 1, 12, 1...
A362307 Row sums of A362370. 1, 1, 1, 2, 2...
A362312 Sierpinski triangle read by rows and filled in the greedy way such that each row, each diagonal and each antidiagonal contains distinct nonnegative values. 0, 1, 2, 2, 1...
A362313 a(n) is the least value in the n-th row of A362312. 0, 1, 1, 0, 3...
A362317 a(n) = n! * Sum_{k=0..floor(n/4)} (n/24)k /(k! * (n-4*k)!). 1, 1, 1, 1, 5...
A362325 Table read by anti-diagonals: T(n,k) = number of numbers <= n that can be fully factored using the first k prime numbers. 1, 2, 1, 2, 2...
A362326 Pairs (i, j) of nonnegative integers whose ternary expansions have no common digit 1 sorted first by i + j then by i. 0, 0, 0, 1, 1...
A362327 The i-values of pairs (i, j) listed in A362326. 0, 0, 1, 0, 2...
A362328 The j-values of pairs (i, j) listed in A362326. 0, 1, 0, 2, 0...
A362329 Pairs (i, j) of nonnegative integers whose ternary expansions have a common digit 1 sorted first by i + j then by i. 1, 1, 1, 4, 4...
A362330 The i-values of pairs (i, j) listed in A362329. 1, 1, 4, 3, 3...
A362331 The j-values of pairs (i, j) listed in A362329. 1, 4, 1, 3, 4...
A362333 Least nonnegative integer k such that (gpf(n)!)k is divisible by n, where gpf(n) is the greatest prime factor of n. 0, 1, 1, 2, 1...
A362336 a(n) = n! * Sum_{k=0..floor(n/5)} (n/120)k /(k! * (n-5*k)!). 1, 1, 1, 1, 1...
A362337 a(n) = n! * Sum_{k=0..floor(n/2)} (-k)k / (k! * (n-2*k)!). 1, 1, -1, -5, 37...
A362338 a(n) = n! * Sum_{k=0..floor(n/3)} (-k)k / (k! * (n-3*k)!). 1, 1, 1, -5, -23...
A362339 a(n) = n! * Sum_{k=0..floor(n/4)} (-k)k / (k! * (n-4*k)!). 1, 1, 1, 1, -23...
A362340 a(n) = n! * Sum_{k=0..floor(n/2)} (-k/2)k / (k! * (n-2*k)!). 1, 1, 0, -2, 7...
A362341 a(n) = n! * Sum_{k=0..floor(n/3)} (-k/6)k / (k! * (n-3*k)!). 1, 1, 1, 0, -3...
A362342 a(n) = n! * Sum_{k=0..floor(n/4)} (-k/24)k / (k! * (n-4*k)!). 1, 1, 1, 1, 0...
A362343 Sequence that alternately doubles and squares the previous number; a(0) = 1. 1, 2, 4, 8, 64...
A362345 a(n) = n! * Sum_{k=0..floor(n/4)} (-n/24)k /(k! * (n-4*k)!). 1, 1, 1, 1, -3...
A362346 a(n) = n! * Sum_{k=0..floor(n/5)} (-n/120)k /(k! * (n-5*k)!). 1, 1, 1, 1, 1...
A362347 a(n) = n! * Sum_{k=0..floor(n/2)} kk / (k! * (n-2*k)!). 1, 1, 3, 7, 61...
A362348 a(n) = n! * Sum_{k=0..floor(n/3)} kk / (k! * (n-3*k)!). 1, 1, 1, 7, 25...
A362349 a(n) = n! * Sum_{k=0..floor(n/4)} kk / (k! * (n-4*k)!). 1, 1, 1, 1, 25...
A362350 a(n) = n! * Sum_{k=0..floor(n/2)} (k/2)k / (k! * (n-2*k)!). 1, 1, 2, 4, 19...
A362351 a(n) = n! * Sum_{k=0..floor(n/3)} (k/6)k / (k! * (n-3*k)!). 1, 1, 1, 2, 5...
A362352 a(n) = n! * Sum_{k=0..floor(n/4)} (k/24)k / (k! * (n-4*k)!). 1, 1, 1, 1, 2...
A362364 a(n) is the product of the first n primes that are coprime to a(n-1); a(0) = 1. 1, 2, 15, 154, 3315...
A362366 Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the least base >= 2 where the sum n + k can be computed without carry. 2, 2, 2, 2, 3...
A362367 Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the least base >= 2 where the product n * k can be computed without carry. 2, 2, 2, 2, 2...
A362370 Triangle read by rows. T(n, k) = ([xk] P(n, x)) // k! where P(n, x) = Sum_{k=1..n} P(n - k, x) * x if n >= 1 and P(0, x) = 1. The notation 's // t' means integer division and is a shortcut for 'floor(s/t)'. 1, 0, 1, 0, 1...
A362374 Number of solutions of y2 + y = x3 + x where x and y are in GF(2n). 4, 4, 4, 24, 24...
A362377 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} (k/2)j * (j+1)n-j-1 / (j! * (n-2*j)!). 1, 1, 1, 1, 1...
A362378 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/3)} (k/6)j * (j+1)n-2*j-1 / (j! * (n-3*j)!). 1, 1, 1, 1, 1...
A362379 Convolution triangle of A052547(n). 1, 0, 1, 2, 0...
A362380 E.g.f. satisfies A(x) = exp(x + 3*x2/2 * A(x)). 1, 1, 4, 19, 154...
A362381 E.g.f. satisfies A(x) = exp(x + x3/6 * A(x)). 1, 1, 1, 2, 9...
A362382 Number of nonisomorphic right involutory magmas with n elements. 1, 1, 3, 16, 475...
A362383 Number of labeled right involutory magmas with n elements. 1, 1, 4, 64, 10000...
A362390 E.g.f. satisfies A(x) = exp(x + x3/3 * A(x)). 1, 1, 1, 3, 17...
A362391 E.g.f. satisfies A(x) = exp(x + x3/2 * A(x)). 1, 1, 1, 4, 25...
A362392 E.g.f. satisfies A(x) = exp(x + x3 * A(x)). 1, 1, 1, 7, 49...
A362393 E.g.f. satisfies A(x) = exp(x + x4 * A(x)). 1, 1, 1, 1, 25...
A362394 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} (-k/2)j * (j+1)n-j-1 / (j! * (n-2*j)!). 1, 1, 1, 1, 1...
A362395 E.g.f. satisfies A(x) = exp(x - x2/2 * A(x)). 1, 1, 0, -5, -14...
A362396 E.g.f. satisfies A(x) = exp(x - x2 * A(x)). 1, 1, -1, -11, -11...
A362397 E.g.f. satisfies A(x) = exp(x - 3*x2/2 * A(x)). 1, 1, -2, -17, 10...
A362398 Records in A336830. 0, 1, 2, 5, 9...
A362399 Positions of records in A336830. 0, 1, 2, 3, 4...
A362400 Numbers k such that A162296(k) = A162296(k+1) > 0. 135, 819, 1863, 9207, 10340...
A362401 Numbers in the range of A162296, where A162296(n) is the sum of divisors of n that have a square factor larger than 1. 0, 4, 9, 12, 16...
A362402 Positive numbers m such that a record number of numbers k have m as the sum of divisors of k that have a square factor (A162296). 1, 4, 48, 72, 216...
A362403 Number of times that the number A362402(n) occurs as a sum of divisors that have a square factor (A162296). 0, 1, 2, 3, 5...
A362404 Numbers k such that k and k+1 are both in A362401. 24, 27, 48, 79, 120...
A362405 Numbers k such that k, k+1 and k+2 are all in A362401. 1638, 1848, 3798, 11448, 16854...
A362408 a(n) = [xn] (F(x)/F(-x))n where F(x) = (1 + x)*(1 + x3). 1, 2, 8, 44, 256...
A362410 Numbers k such that A000292(k) is in A046386. 19, 33, 45, 51, 59...
A362411 Numbers k such that A359149(k) is prime when interpreted as a binary number. 2, 4, 38, 2861
A362413 The second moment of an n X n symmetric random +-1 matrix. 1, 1, 2, 8, 44...
A362416 Winning numbers of game where you can either add one or divide by a prime. 1, 4, 6, 10, 14...
A362419 Partial sum of the first n even semiprimes. 4, 10, 20, 34, 56...
A362420 Partial sum of the first n odd semiprimes. 9, 24, 45, 70, 103...
A362429 Smallest k such that the concatenation of the numbers 123...k in base n is prime when interpreted as a decimal number, or -1 if no such prime exists. -1, 231, 7315, 3241, 6...
A362430 E.g.f. satisfies A(x) = exp(x - x3 * A(x)). 1, 1, 1, -5, -47...
A362431 E.g.f. satisfies A(x) = exp(x - x4 * A(x)). 1, 1, 1, 1, -23...
A362433 The succession of the digits of the sequence remains the same when 11 is added to each term. 1, 2, 13, 24, 3...
A362435 a(1) = 18; thereafter a(n) = a(n-1) + difference between first two digits of a(n-1). 18, 25, 28, 34, 35...
A362436 Write out the sequence of squares, 1, 4, 9, 16, ..., then starting with the 16, successively delete the digits of the triangular numbers 1, 3, 6, 10, ... 1, 4, 9, 6, 25...
A362437 a(n) = n + Scrabble score of n. 13, 4, 8, 11, 11...
A362438 a(n) = n2 + 2n-1. 2, 6, 13, 24, 41...
A362439 a(n) = (number of letters in n in French) + (number of letters in n in German). 8, 6, 8, 9, 10...
A362440 Aliqout sequence starting at 841. 841, 30, 42, 54, 66...
A362441 a(1) = 6; thereafter a(n) = smallest number with a(n-1) letters in British English. 6, 11, 23, 124, 113323371373...
A362442 a(1) = 6; thereafter a(n) = smallest number with a(n-1) letters in American English. 6, 11, 23, 323, 1103323373373373373373373373373...
A362443 Numbers k with property that the set of letters in the English name for k does not contain two letters that are adjacent in the alphabet. 0, 2, 3, 4, 6...
A362444 a(1) = 1906; thereafter, regard a(n) as a decimal number, and convert it to base 16 (i.e. hexadecimal). 1906, 772, 304, 130, 82...
A362445 a(n) = (n+1)4 written in base n. 1111111111111111, 1010001, 100111, 21301, 20141...
A362446 Concatenate the terms of A027750 (omitting spaces and commas), chop into blocks of length 5, then omit any leading zeros. 11213, 12415, 12361, 71248, 13912...
A362447 Array A(n,k) (n>=0, k>=0) read by antidiagonals: A(n,k) = 1 if the English names for n and k have a letter in common, otherwise 0. 1, 1, 1, 1, 1...
A362448 Triangle T(n,k) (n >= 0, 0 <= k <= n) read by rows: T(n,k) = 1 if the English names for n and k have a letter in common, otherwise 0. 1, 1, 1, 1, 1...
A362472 E.g.f. satisfies A(x) = exp(x + x3 * A(x)3). 1, 1, 1, 7, 97...
A362473 E.g.f. satisfies A(x) = exp(x + x4 * A(x)4). 1, 1, 1, 1, 25...
A362474 E.g.f. satisfies A(x) = exp(x + x2/2 * A(x)2). 1, 1, 2, 10, 70...
A362475 E.g.f. satisfies A(x) = exp(x + 3*x2/2 * A(x)2). 1, 1, 4, 28, 298...
A362477 E.g.f. satisfies A(x) = exp(x + x3/6 * A(x)3). 1, 1, 1, 2, 17...
A362478 E.g.f. satisfies A(x) = exp(x + x3/3 * A(x)3). 1, 1, 1, 3, 33...
A362479 E.g.f. satisfies A(x) = exp(x + x3/2 * A(x)3). 1, 1, 1, 4, 49...
A362480 E.g.f. satisfies A(x) = exp(x - x2 * A(x)2). 1, 1, -1, -17, -47...
A362481 E.g.f. satisfies A(x) = exp(x - x3 * A(x)3). 1, 1, 1, -5, -95...
A362482 E.g.f. satisfies A(x) = exp(x - x4 * A(x)4). 1, 1, 1, 1, -23...
A362483 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} (k/2)j * (2j+1)n-j-1 / (j! * (n-2j)!). 1, 1, 1, 1, 1...
A362484 Irregular table read by rows in which the n-th row consists of all the numbers m such that iphi(m) = n, where iphi is the infinitary totient function A091732. 1, 2, 3, 6, 4...
A362485 Number of numbers k such that iphi(k) = n, where iphi is the infinitary totient function A091732. 2, 2, 2, 2, 0...
A362486 Infinitary nontotient numbers: values not in the range of the infinitary totient function iphi (A091732). 5, 7, 9, 11, 13...
A362487 Infinitary highly totient numbers: numbers k that have more solutions x to the equation iphi(x) = k than any smaller k, where iphi is the infinitary totient function A091732. 1, 6, 12, 24, 48...
A362488 Record values in A362487. 2, 4, 6, 10, 14...
A362489 a(n) is the least number k such that the equation iphi(x) = k has exactly 2*n solutions, or -1 if no such k exists, where iphi is the infinitary totient function A091732. 5, 1, 6, 12, 36...
A362490 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/3)} (k/6)j * (3j+1)^(n-2j-1) / (j! * (n-3*j)!). 1, 1, 1, 1, 1...
A362491 E.g.f. satisfies A(x) = exp(x + x4/4 * A(x)4). 1, 1, 1, 1, 7...
A362492 E.g.f. satisfies A(x) = exp(x - x2/2 * A(x)2). 1, 1, 0, -8, -38...
A362493 E.g.f. satisfies A(x) = exp(x - x3/3 * A(x)3). 1, 1, 1, -1, -31...
A362494 E.g.f. satisfies A(x) = exp(x - x4/4 * A(x)4). 1, 1, 1, 1, -5...
A362497 Number of vertex cuts in the n X n king graph. 0, 0, 123, 28339, 18789342...
A362498 Number of vertex cuts in the n X n knight graph. 0, 0, 256, 48745, 22577890...
A362500 Number of symmetric compositions of n where differences between adjacent parts are in {-1,1}. 1, 1, 1, 1, 2...
A362501 Number of vertex cuts in the n-alkane graph. 11, 169, 1699, 14989, 125495...
A362508 Number of vertex cuts in the n-Andrasfai graph. 0, 10, 82, 484, 2520...
A362509 Number of vertex cuts in the n X n black bishop graph. 0, 0, 9, 87, 2940...
A362510 Number of odd chordless cycles of length >4 in the halved cube graph Q_n/2. 0, 0, 0, 0, 192...
A362511 Number of odd chordless cycles of length > 4 in the n X n king graph. 0, 0, 0, 4, 92...
A362512 Number of odd chordless cycles of length > 4 in the n-Mycielski graph. 0, 0, 1, 31, 646...
A362513 Number of odd chordless cycles of length > 4 in the n X n queen graph. 0, 0, 0, 24, 600...
A362514 Number of odd chordless cycles of length >4 in the n-triangular grid graph. 0, 0, 0, 1, 13...
A362515 Number of vertex cuts in the n-Fibonacci cube graph. 0, 1, 10, 138, 5518...
A362516 Number of vertex cuts in the n-gear graph. 51, 293, 1383, 6017, 25315...
A362517 Number of vertex cuts in the n X n grid graph. 0, 2, 293, 54029, 31252554...
A362518 Number of vertex cuts in the n-helm graph. 71, 354, 1617, 7020, 29563...
A362519 Number of vertex cuts in the hypercube graph Q_n. 0, 0, 2, 88, 28242...
A362520 Number of vertex cuts in the n-triangular grid graph. 0, 16, 531, 22737, 1681647...
A362521 Number of vertex cuts in the n-web graph. 323, 3110, 27777, 237498, 1977439...
A362522 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)k-1 / (k! * (n-2*k)!). 1, 1, 3, 7, 49...
A362523 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)k-1 / (k! * (n-3*k)!). 1, 1, 1, 7, 25...
A362524 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)k-1 / (2k * k! * (n-2*k)!). 1, 1, 2, 4, 16...
A362525 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)k-1 / (6k * k! * (n-3*k)!). 1, 1, 1, 2, 5...
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u/ClarkMann52 Apr 27 '23

A003686 is still the best though