A300704 Number of compositions (ordered partitions) of n into prime power parts (not including 1) that do not divide n.
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
Offset: 0
Keywords
Examples
a(10) = 5 because we have [7, 3], [4, 3, 3], [3, 7], [3, 4, 3] and [3, 3, 4].
Links
Programs
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Maple
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: seq(a(n), n=0..70); # Alois P. Heinz, Mar 11 2018 -
Mathematica
Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 48}]