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

1,4

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A163118 A319010 A010762 * A309912 A222734 A151888

Adjacent sequences: A055990 A055991 A055992 * A055994 A055995 A055996

Keyword

nonn

Author

Labos Elemer, Jul 21 2000

Status

approved