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Search: id:A056672
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| A056672 |
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Number of unitary and square-free divisors of n! Also, number of divisors of the special square-free part of n!, A055773(n). |
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+0
1
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| 1, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 8, 4, 4, 4, 8, 8, 16, 16, 16, 8, 16, 16, 16, 8, 8, 8, 16, 16, 32, 32, 32, 16, 16, 16, 32, 16, 16, 16, 32, 32, 64, 64, 64, 32, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 64, 128, 128, 256, 128, 128, 128, 128, 128, 256, 256, 256, 256
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OFFSET
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1,2
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COMMENT
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The divisor d=1 is counted here as being free of prime divisors and also unitary.
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FORMULA
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a(n)=A000005[A055231(n!)]=A000005[A007913(n!)/A055229(n!)]= a(n)=A000005[A055773(n)]
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EXAMPLE
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n=11, 11!=2.2.2.2.2.2.2.2.3.3.3.3.5.5.7.11, has 540 divisors, 32 are unitary and 32 are square-free. Only 4 divisors, {1,7,11,77} have both properties, so a(11)=4.
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CROSSREFS
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A000005, A055231, A007913, A055229, A055773, A000142.
Sequence in context: A158137 A010694 A111737 this_sequence A037201 A128886 A031883
Adjacent sequences: A056669 A056670 A056671 this_sequence A056673 A056674 A056675
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 10 2000
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