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A055993 Number of square divisors of n!. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)