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 A384226 #26 Aug 13 2025 15:06:08 %S A384226 1,1,1,3,1,1,5,4,1,7,1,1,3,9,1,5,1,11,4,1,13,1,7,1,8,15,1,1,17,13,1, %T A384226 19,6,1,3,7,21,1,11,1,23,4,1,5,25,1,13,1,3,9,27,8,1,29,24,1,31,1,1,3, %U A384226 11,33,1,17,1,12,35,13,1,37,1,19,1,3,13,39,6,1,41,32,1,43,1,11,1,32,45,1,23,1,47,4 %N A384226 Irregular triangle read by rows: T(n,k) is the sum of odd divisors in the k-th 2-dense sublist of divisors of n, with n >= 1, k >= 1. %C A384226 T(n,k) is the sum of odd numbers in the k-th sublist (or subsequence) of divisors of n such that the ratio of adjacent divisors in every sublist is at most 2. %C A384226 In a sublist of divisors of n the terms are in increasing order and two adjacent terms are the same two adjacent terms in the list of divisors of n. %C A384226 It shares the odd-indexed rows with A384149. %C A384226 At least for the first 1000 rows the row lengths give A237271. %H A384226 Paolo Xausa, <a href="/A384226/b384226.txt">Table of n, a(n) for n = 1..10607</a> (rows 1..3500 of triangle, flattened). %e A384226 -------------------------------------------------------------------- %e A384226 | n | Row n of | List of divisors of n | Number of | %e A384226 | | the triangle | [with sublists in brackets] | sublists | %e A384226 -------------------------------------------------------------------- %e A384226 | 1 | 1; | [1]; | 1 | %e A384226 | 2 | 1; | [1, 2]; | 1 | %e A384226 | 3 | 1, 3; | [1], [3]; | 2 | %e A384226 | 4 | 1; | [1, 2, 4]; | 1 | %e A384226 | 5 | 1, 5; | [1], [5]; | 2 | %e A384226 | 6 | 4; | [1, 2, 3, 6]; | 1 | %e A384226 | 7 | 1, 7; | [1], [7]; | 2 | %e A384226 | 8 | 1; | [1, 2, 4, 8]; | 1 | %e A384226 | 9 | 1, 3, 9; | [1], [3], [9]; | 3 | %e A384226 | 10 | 1, 5; | [1, 2], [5, 10]; | 2 | %e A384226 | 11 | 1, 11; | [1], [11]; | 2 | %e A384226 | 12 | 4; | [1, 2, 3, 4, 6, 12]; | 1 | %e A384226 | 13 | 1, 13; | [1], [13]; | 2 | %e A384226 | 14 | 1, 7; | [1, 2], [7, 14]; | 2 | %e A384226 | 15 | 1, 8, 15; | [1], [3, 5], [15]; | 3 | %e A384226 | 16 | 1; | [1, 2, 4, 8, 16]; | 1 | %e A384226 | 17 | 1, 17; | [1], [17]; | 2 | %e A384226 | 18 | 13; | [1, 2, 3, 6, 9, 18]; | 1 | %e A384226 | 19 | 1, 19; | [1], [19]; | 2 | %e A384226 | 20 | 6; | [1, 2, 4, 5, 10, 20]; | 1 | %e A384226 | 21 | 1, 3, 7, 21; | [1], [3], [7], [21]; | 4 | %e A384226 ... %e A384226 For n = 14 the list of divisors of 14 is [1, 2, 7, 14]. There are two sublists of divisors of 14 whose terms increase by a factor of at most 2, they are [1, 2] and [7, 14]. The sums of odd terms in the sublists are [1], [7] respectively, so the row 14 is [1, 7]. %e A384226 For n = 15 the list of divisors of 15 is [1, 3, 5, 15]. There are three sublists of divisors of 15 whose terms increase by a factor of at most 2, they are [1], [3, 5], [15]. The sums of terms in the sublists are [1, 8, 15] respectively, so the row 15 is [1, 8, 15]. %e A384226 For n = 16 the list of divisors of 16 is [1, 2, 4, 8, 16]. There is only one sublist of divisors of 16 whose terms increase by a factor of at most 2, that is the same as the list of divisors of 16, so the row 16 is [1]. %e A384226 For n = 2350 the list of divisors of 2350 is [1, 2, 5, 10, 25, 47, 50, 94, 235, 470, 1175, 2350]. There are five sublists of divisors of 2350 whose terms increase by a factor of at most 2, they are [1, 2], [5, 10], [25, 47, 50, 94], [235, 470], [1175, 2350]. The sums of odd terms in the sublists are [1, 5, 72, 235, 1175] respectively, so the row 2350 is [1, 5, 72, 235, 1175]. %t A384226 A384226row[n_] := Map[Total[Select[#, OddQ]] &, Split[Divisors[n], #2/# <= 2 &]]; %t A384226 Array[A384226row, 50] (* _Paolo Xausa_, Jul 08 2025 *) %Y A384226 Row sums give A000593. %Y A384226 Cf. A174973 (2-dense numbers), A237271, A237593, A379288, A384149, A384222, A384225, A384928. %K A384226 nonn,tabf %O A384226 1,4 %A A384226 _Omar E. Pol_, Jun 24 2025