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%I #14 May 25 2024 19:41:07
%S 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 15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,
%U 26,28,28,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37
%N Largest k such that (k!)^2 divides n!.
%C 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 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 Amiram Eldar, <a href="/A056039/b056039.txt">Table of n, a(n) for n = 1..10000</a>
%F A105350(n) = A001044(a(n)).
%t a[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; k - 1]; Array[a, 100] (* _Amiram Eldar_, May 24 2024 *)
%Y Cf. A000142, A001057, A001405, A055772, A056038, A056067, A056068.
%Y Cf. A001044, A105350.
%K nonn
%O 1,4
%A _Labos Elemer_, Jul 25 2000
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