This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383962 #12 May 30 2025 16:05:52 %S A383962 1,1,1,2,1,1,2,1,3,1,2,1,1,2,3,1,3,1,2,1,3,1,2,1,3,1,2,3,4,1,1,2,1,3, %T A383962 5,1,2,1,4,1,2,3,4,1,3,1,2,1,3,1,2,3,1,3,1,2,3,4,1,4,1,2,1,3,4,7,1,2, %U A383962 1,1,2,3,4,1,3,1,2,3,4,1,3,6,1,2,1,3,1,2,3,4,1,4,1,2,1,3,5,7,1,2,1,4,1,2,3,4,5,6 %N A383962 Irregular triangle read by rows: T(n,k) is the index of the k-th odd divisor in the list of divisors of n, with n >= 1, k >= 1. %C A383962 Row n lists the indices of the odd divisors in the list of divisors of n. %C A383962 If n is odd then row n lists the first A000005(n) positive integers (A000027). %C A383962 Row n is [1] if and only if n is a power of 2 (A000079). %C A383962 Row n is [1, 2] if and only if n is an odd prime (A065091). %e A383962 Triangle begins (n = 1..21): %e A383962 1; %e A383962 1; %e A383962 1, 2; %e A383962 1; %e A383962 1, 2; %e A383962 1, 3; %e A383962 1, 2; %e A383962 1; %e A383962 1, 2, 3; %e A383962 1, 3; %e A383962 1, 2; %e A383962 1, 3; %e A383962 1, 2; %e A383962 1, 3; %e A383962 1, 2, 3, 4; %e A383962 1; %e A383962 1, 2; %e A383962 1, 3, 5; %e A383962 1, 2; %e A383962 1, 4; %e A383962 1, 2, 3, 4; %e A383962 ... %e A383962 For n = 20 the divisors of 20 are [1, 2, 4, 5, 10, 20]. The odd divisors are [1, 5] and their indices in the list of divisors are [1, 4] respectively, so the 20th row of the triangle is [1, 4]. %t A383962 row[n_] := Position[Divisors[n], _?OddQ] // Flatten; Array[row, 45] // Flatten (* _Amiram Eldar_, May 26 2025 *) %Y A383962 Column 1 gives A000012. %Y A383962 Row lengths gives A001227. %Y A383962 Right border gives A383401. %Y A383962 Cf. A000005, A000027, A000079, A027750, A065091, A174090, A182469. %K A383962 nonn,tabf %O A383962 1,4 %A A383962 _Omar E. Pol_, May 26 2025