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A056630
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Number of non-unitary square divisors of n!.
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0
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0, 0, 0, 1, 1, 2, 2, 4, 8, 22, 22, 28, 28, 56, 88, 120, 120, 172, 172, 284, 292, 584, 584, 848, 1136, 2272, 2656, 4304, 4304, 5312, 5312, 6080, 6112, 12992, 16256, 19376, 19376, 38752, 43136, 47936, 47936, 63936, 63936, 100672, 132928, 278528, 278528
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OFFSET
| 1,6
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FORMULA
| a(n)=A046951(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 22 is not unitary [but squares]: {4,9,16,36,64,100,144,225,324,400,576,...,57600,129600}. E.g. GCD[576,10!/576]=GCD[576,6300]=36. Thus a(10)=30-8=22.
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CROSSREFS
| Cf. A055993, A048656, A056657, A000188, A008833, A055229, A046951, A055230, A055071, A001221.
Sequence in context: A005702 A095335 A100396 * A121853 A064451 A032440
Adjacent sequences: A056627 A056628 A056629 * A056631 A056632 A056633
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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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