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A112624
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If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = product_{p|n} b(p,n)!.
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1
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1, 1, 1, 2, 1, 1, 1, 6, 2, 1, 1, 2, 1, 1, 1, 24, 1, 2, 1, 2, 1, 1, 1, 6, 2, 1, 6, 2, 1, 1, 1, 120, 1, 1, 1, 4, 1, 1, 1, 6, 1, 1, 1, 2, 2, 1, 1, 24, 2, 2, 1, 2, 1, 6, 1, 6, 1, 1, 1, 2, 1, 1, 2, 720, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 2, 2, 1, 1, 1, 24, 24, 1, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 1, 1, 120, 1, 2, 2, 4, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The logarithm of the Dirichlet series with the reciprocals of this sequence as coefficients, is the Dirichlet series with the characteristic function of primes A010051 as coefficients.
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EXAMPLE
| 45 = 3^2 * 5^1. So a(45) = 2! * 1! = 2.
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MATHEMATICA
| f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Times @@ (fi!)]; Array[f, 101] (* Robert G. Wilson v *)
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CROSSREFS
| For row > 1: a(n) = row products of A100995(A126988), when neglecting zero elements.
Sequence in context: A156233 A060185 A129110 * A139329 A069777 A064992
Adjacent sequences: A112621 A112622 A112623 * A112625 A112626 A112627
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KEYWORD
| nonn,mult
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AUTHOR
| Leroy Quet, Dec 25 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 27 2005
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