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1, 0, 1, 2, 4, 5, 10, 12, 20, 25, 41, 47, 76, 90, 129, 161, 230, 270, 384, 458, 615, 750, 1001, 1187, 1570, 1881, 2414, 2907, 3717, 4400, 5603, 6666, 8306, 9912, 12295, 14537, 17976, 21252, 25937, 30683, 37337, 43861, 53173, 62467, 75020, 88132
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OFFSET
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1,4
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COMMENTS
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A000041 = (1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, ...).
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LINKS
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FORMULA
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Möbius transform of A000041, the partition numbers.
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EXAMPLE
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a(4) = 2 = (0, -1, 0, 1) dot (1, 1, 2, 3) = (0, -1, 0, 3).
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MAPLE
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read("transforms") : A000041 := proc(n) combinat[numbpart](n) ; end: a000041 := [seq(A000041(n), n=0..150)] ; a133732 := MOBIUS(a000041) ; # R. J. Mathar, Jan 19 2009
mob := (m, n) -> if irem(m, n) = 0 then numtheory:-mobius(m/n) else 0 fi:
A133732 := n -> add(mob(n, d)*combinat:-numbpart(d-1), d=1..n):
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MATHEMATICA
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a[n_] := DivisorSum[n, MoebiusMu[n/#]*PartitionsP[#-1]&];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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