A055993 Number of square divisors of n!.

1, 1, 1, 2, 2, 6, 6, 8, 12, 30, 30, 36, 36, 72, 96, 128, 128, 180, 180, 300, 300, 600, 600, 864, 1152, 2304, 2688, 4368, 4368, 5376, 5376, 6144, 6144, 13056, 16320, 19440, 19440, 38880, 43200, 48000, 48000, 64000, 64000, 100800, 133056, 278784, 278784

Offset: 1

Author

Labos Elemer, Jul 21 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000142, A000005, A046951, A055772, A000188.

Programs

Mathematica

Table[Count[Divisors[n!], d_ /; IntegerQ@ Sqrt@ d], {n, 30}] (* Michael De Vlieger, Feb 05 2017 *)

PARI

a(n) = sumdiv(n!, d, issquare(d)); \\ Michel Marcus, Dec 26 2013

Formula

a(n) = A046951(n!) = A000005(A055772(n)) = A000005(A000188(A000142(n))).