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A056629 Number of unitary square divisors of n!. 0
1, 1, 1, 1, 1, 4, 4, 4, 4, 8, 8, 8, 8, 16, 8, 8, 8, 8, 8, 16, 8, 16, 16, 16, 16, 32, 32, 64, 64, 64, 64, 64, 32, 64, 64, 64, 64, 128, 64, 64, 64, 64, 64, 128, 128, 256, 256, 256, 256, 256, 128, 256, 256, 256, 256, 256, 128, 256, 256, 256, 256, 512, 512, 512, 512, 512 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Unitary analog of A046951(n!) = A055993(n).

LINKS

Table of n, a(n) for n=1..66.

FORMULA

a(n)=2^r, where r is the number of prime divisors of unitary analog of largest square divisor of n!. r(n)=A001221[A000188(n!)/A055229(n!)]

EXAMPLE

n=10 and the largest square-root divisor of 10! is 720. 10! has 30 square divisors, of which 8 is unitary [and squares]: {1,25,81,256,2025,6400,20736,518400}. E.g. GCD[256,10!/256]=GCD[256,14175]=1. Thus a(10)=8.

CROSSREFS

Cf. A055993, A048656, A056657, A000188, A008833, A055229, A046951, A055230, A055071, A001221.

Sequence in context: A240835 A047210 A120327 * A245356 A167185 A081676

Adjacent sequences:  A056626 A056627 A056628 * A056630 A056631 A056632

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 08 2000

STATUS

approved

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Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.