%I #13 May 26 2024 09:18:32

%S 416,417,916,917,1974,1975,2440,2441,2910,2911,3194,3195,3778,3779,

%T 4024,4025,4288,4289,4660,4661,4954,4955,5326,5327,5982,5983,6706,

%U 6707,6830,6831,6860,6861,6878,6879,6950,6951,6952,6953,7102,7103,7126,7127

%N Numbers k such that k! is divisible by the square of (f+d)!^2 for d = 0, 1 and 2 (and possibly larger d), where f = floor(k/2).

%C Numbers k such that A056039(k) > floor(k/2) + 1. - _Amiram Eldar_, May 24 2024

%H Amiram Eldar, <a href="/A056068/b056068.txt">Table of n, a(n) for n = 1..10000</a>

%t q[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; k - 1] > Floor[n/2] + 1; Select[Range[7200], q] (* _Amiram Eldar_, May 24 2024 *)

%Y Cf. A056038, A056039, A056042, A056043, A056044.

%Y Subsequence of A056067.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 26 2000