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%I #9 Mar 16 2018 08:28:59
%S 1,0,0,0,0,2,0,7,2,7,5,46,2,115,20,39,16,723,16,1819,27,559,414,11481,
%T 16,13204,1763,6450,383,181548,172,455646,1326,70476,29809,571110,275,
%U 7203906,121535,739513,1703,45380391,7362,113898438,65049,757426,2009203,717490902,2304
%N Number of compositions (ordered partitions) of n into prime power parts (not including 1) that do not divide n.
%H Alois P. Heinz, <a href="/A300704/b300704.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e a(10) = 5 because we have [7, 3], [4, 3, 3], [3, 7], [3, 4, 3] and [3, 3, 4].
%p a:= proc(m) option remember; local b; b:= proc(n) option
%p remember; `if`(n=0, 1, add(`if`(nops(ifactors(j)[2])
%p <>1 or irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
%p end:
%p seq(a(n), n=0..70); # _Alois P. Heinz_, Mar 11 2018
%t Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 48}]
%Y Cf. A246655, A280195, A284465, A300580, A300584, A300702, A300703, A300706.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Mar 11 2018
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