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 A376248 #20 Oct 13 2024 11:21:30
%S A376248 1,1,2,1,3,1,2,4,1,5,1,2,3,4,6,9,1,7,1,2,4,8,1,3,9,1,2,4,5,10,25,1,11,
%T A376248 1,2,3,4,6,8,9,12,18,27,1,13,1,2,4,7,14,49,1,3,5,9,15,25,1,2,4,8,16,1,
%U A376248 17,1,2,3,4,6,8,9,12,18,27,1,19,1,2,4,5,8,10,20,25,50,125
%N A376248 Irregular triangle where row n lists m such that rad(m) | n and bigomega(m) <= bigomega(n), where rad = A007947 and bigomega = A001222.
%C A376248 Analogous to A162306 regarding m such that rad(m) | n, but instead of taking m <= n, we take m such that bigomega(m) <= bigomega(n).
%C A376248 Row n is a finite set of products of prime power factors p^k (i.e., p^k | n) such that Sum_{p|n} k <= bigomega(n).
%C A376248 For prime power n = p^k, k >= 0 (i.e., n in A000961), row p^k of this sequence is the same as row p^k of A027750 and A162306. Therefore, for prime p, row p of this sequence is the same as row p of A027750 and A162306: {1, p}.
%C A376248 For n in A024619, row n of this sequence does not match row n of A162306, since the former contains gpf(n)^bigomega(n) = A006530(n)^A001222(n), which is larger than n.
%H A376248 Michael De Vlieger, <a href="/A376248/b376248.txt">Table of n, a(n) for n = 1..17475</a> (rows n = 1..1000, flattened)
%H A376248 Michael De Vlieger, <a href="/A376248/a376248.png">Log log scatterplot of rows n = 1..2^16 of this sequence, flattened</a>, (3153752 terms).
%F A376248 Row n of this sequence is { m : rad(m) | n, bigomega(m) <= bigomega(n) }.
%F A376248 A376567(n) = binomial(bigomega(n) + omega(n)) = Length of row n, where omega = A001221.
%e A376248 Triangle begins:
%e A376248 n row n of this sequence:
%e A376248 -------------------------------------------
%e A376248 1: 1;
%e A376248 2: 1, 2;
%e A376248 3: 1, 3;
%e A376248 4: 1, 2 4;
%e A376248 5: 1, 5;
%e A376248 6: 1, 2, 3, 4, 6, 9;
%e A376248 7: 1, 7;
%e A376248 8: 1, 2, 4, 8;
%e A376248 9: 1, 3, 9;
%e A376248 10: 1, 2, 4, 5, 10, 25;
%e A376248 11: 1, 11;
%e A376248 12: 1, 2, 3, 4, 6, 8, 9, 12, 18, 27;
%e A376248 ...
%e A376248 Row n = 10 of this sequence, presented according to 2^k, k = 0..bigomega(n) by columns, 5^i, i = 0..bigomega(n) by rows, showing terms m > n with an asterisk. The remaining m and the parenthetic 8 are in row 10 of A162306:
%e A376248 1 2 4 (8)
%e A376248 5 10
%e A376248 25*
%e A376248 Row n = 12 of this sequence, presented according to 2^k, k = 0..bigomega(n) by columns, 3^i, i = 0..bigomega(n) by rows, showing terms m > n with an asterisk. The remaining m are in row 12 of A162306:
%e A376248 1 2 4 8
%e A376248 3 6 12
%e A376248 9 18*
%e A376248 27*
%t A376248 Table[Clear[p]; MapIndexed[Set[p[First[#2]], #1] &, FactorInteger[n][[All, 1]]]; k = PrimeOmega[n]; w = PrimeNu[n]; Union@ Map[Times @@ MapIndexed[p[First[#2]]^#1 &, #] &, Select[Tuples[Range[0, k], w], Total[#] <= k &] ], {n, 120}]
%Y A376248 Cf. A000961, A001221, A001222, A006530, A007947, A010846, A024619, A027750, A162306, A376567.
%K A376248 nonn,tabf
%O A376248 1,3
%A A376248 _Michael De Vlieger_, Oct 09 2024