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 A056039 #14 May 25 2024 19:41:07
%S A056039 1,1,1,2,2,3,3,4,4,6,6,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,15,15,
%T A056039 15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,
%U A056039 26,28,28,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37
%N A056039 Largest k such that (k!)^2 divides n!.
%C A056039 Let d(n) = a(n) - floor(n/2). Then, d(n) >= 0, and below 1000, d=1 arises 93 times, and d=2 arises 4 times.
%C A056039 The first occurrence of d(k) = 0, 1, 2, ..., is at k = 2, 1 (=A056067(1)), 416 (=A056068(1)), 6950, 16348, 505930, ... . - _Amiram Eldar_, May 24 2024
%H A056039 Amiram Eldar, <a href="/A056039/b056039.txt">Table of n, a(n) for n = 1..10000</a>
%F A056039 A105350(n) = A001044(a(n)).
%t A056039 a[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; k - 1]; Array[a, 100] (* _Amiram Eldar_, May 24 2024 *)
%Y A056039 Cf. A000142, A001057, A001405, A055772, A056038, A056067, A056068.
%Y A056039 Cf. A001044, A105350.
%K A056039 nonn
%O A056039 1,4
%A A056039 _Labos Elemer_, Jul 25 2000