A056039 Largest k such that (k!)^2 divides n!.

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, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 28, 28, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37

Offset

1,4

Comments

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.

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

Links

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

Formula

A105350(n) = A001044(a(n)).

Mathematica

a[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; k - 1]; Array[a, 100] (* Amiram Eldar, May 24 2024 *)

Crossrefs

Cf. A000142, A001057, A001405, A055772, A056038, A056067, A056068.

Cf. A001044, A105350.

Sequence in context: A100881 A053263 A317908 * A181972 A356737 A058747

Adjacent sequences: A056036 A056037 A056038 * A056040 A056041 A056042

Keyword

nonn

Author

Labos Elemer, Jul 25 2000

Status

approved