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 A287549 #10 Feb 16 2025 08:33:46 %S A287549 1,2,3,4,5,7,8,10,11,13,14,17,18,20,22,24,25,28,29,32,34,36,37,42,43, %T A287549 45,47,50,51,56,57,60,62,64,66,71,72,74,76,81,82,87,88,91,94,96,97, %U A287549 104,105,108,110,113,114,119,121,126,128,130,131,140,141,143,146,150,152,157,158,161,163,168,169,178,179,181,184 %N A287549 Total number of unordered factorizations of all positive integers <= n into distinct factors greater than 1. %C A287549 Partial sums of A045778. %H A287549 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnorderedFactorization.html">Unordered Factorization</a> %F A287549 a(p^k) = a(p^k-1) + A000009(k), where p is a prime. %e A287549 a(6) = 7 because we have [1], [2], [3], [4], [5], [2*3] and [6] (the factorization [2*2] is not permitted because the factor 2 is present twice). %t A287549 Accumulate[gd[m_, 1] := 1; gd[1, n_] := 0; gd[1, 1] := 1; gd[0, n_] := 0; gd[m_, n_] := gd[m, n] = Total[gd[# - 1, n/#] & /@ Select[Divisors[n], # <= m &]]; Array[ gd[#, #] &, 75]] %Y A287549 Cf. A000009, A001055, A036469, A045778, A086435, A096276. %K A287549 nonn %O A287549 1,2 %A A287549 _Ilya Gutkovskiy_, May 26 2017