A056044 Let k be the largest number such that k^2 divides n! and let m be the largest number such that m!^2 divides n!; a(n) = k/m!.

1, 1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 2, 6, 3, 3, 2, 2, 2, 2, 2, 2, 2, 10, 10, 30, 2, 2, 12, 12, 3, 3, 6, 30, 10, 10, 10, 30, 6, 6, 2, 2, 2, 30, 60, 60, 30, 210, 42, 42, 42, 42, 1, 1, 2, 2, 4, 4, 4, 4, 4, 84, 21, 21, 14, 14, 14, 42, 6, 6, 2, 2, 2, 10, 10, 70, 140, 140, 14, 126, 3, 3, 6, 30

Offset

1,6

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000188(n!)/A056038(n).

Example

For n = 11, 11! = 6! * 6! * 77, so A000188(11!) = A056038(11) = 6! and a(11) = 6!/6! = 1.

Mathematica

f[p_, e_] := p^Floor[e/2]; b[1] = 1; b[n_] := Times @@ f @@@ FactorInteger[n!];
c[n_] := Module[{k = 1}, NestWhile[#/(++k)^2 &, n!, IntegerQ]; (k-1)!];
a[n_] := b[n] / c[n]; Array[a, 100] (* Amiram Eldar, May 24 2024 *)

Crossrefs

Cf. A000188, A055772, A001405, A001057, A056038.

Sequence in context: A116687 A264033 A236293 * A236097 A239319 A236468

Adjacent sequences: A056041 A056042 A056043 * A056045 A056046 A056047

Keyword

nonn

Author

Labos Elemer, Jul 25 2000

Extensions

Name corrected by Amiram Eldar, May 24 2024

Status

approved