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A300704
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Number of compositions (ordered partitions) of n into prime power parts (not including 1) that do not divide n.
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4
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1, 0, 0, 0, 0, 2, 0, 7, 2, 7, 5, 46, 2, 115, 20, 39, 16, 723, 16, 1819, 27, 559, 414, 11481, 16, 13204, 1763, 6450, 383, 181548, 172, 455646, 1326, 70476, 29809, 571110, 275, 7203906, 121535, 739513, 1703, 45380391, 7362, 113898438, 65049, 757426, 2009203, 717490902, 2304
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OFFSET
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0,6
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LINKS
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EXAMPLE
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a(10) = 5 because we have [7, 3], [4, 3, 3], [3, 7], [3, 4, 3] and [3, 3, 4].
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MAPLE
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a:= proc(m) option remember; local b; b:= proc(n) option
remember; `if`(n=0, 1, add(`if`(nops(ifactors(j)[2])
<>1 or irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
end:
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MATHEMATICA
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Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 48}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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