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A056629
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Number of unitary square divisors of n!.
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0
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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; internal format)
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OFFSET
| 1,6
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COMMENTS
| Unitary analogue of A046951(n!)=A055993(n).
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FORMULA
| a(n)=2^r, where r is the number of prime divisors of unitary analogue of largest square divisor of n!. r(n)=A001221[A000188(n!)/A055229(n!)]
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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.
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CROSSREFS
| Cf. A055993, A048656, A056657, A000188, A008833, A055229, A046951, A055230, A055071, A001221.
Sequence in context: A159835 A047210 A120327 * A167185 A081676 A114555
Adjacent sequences: A056626 A056627 A056628 * A056630 A056631 A056632
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 08 2000
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