A056067 - OEIS

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A056067

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

1, 10, 11, 28, 29, 54, 55, 82, 83, 88, 89, 130, 131, 152, 153, 180, 181, 218, 219, 250, 251, 278, 279, 304, 305, 310, 311, 338, 339, 372, 373, 378, 379, 406, 407, 416, 417, 418, 419, 438, 439, 454, 455, 460, 461, 474, 475, 530, 531, 550, 551, 596, 597, 614

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OFFSET

1,2

COMMENTS

Observe that all terms (except 1) are pairs of consecutive numbers starting with an even number (e.g., 88, 89).

Numbers k such that A056039(k) > floor(k/2). - Amiram Eldar, May 24 2024

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

For n = 10 and 11, 10! and 11! are both divisible by 5!^2 and 6!^2.

MATHEMATICA

q[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; k - 1] > Floor[n/2]; Select[Range[620], q] (* Amiram Eldar, May 24 2024 *)