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A341137 Number of ways to write n as an ordered sum of 8 prime powers (including 1).

%I A341137 #6 Feb 05 2021 18:53:33
%S A341137 1,8,36,120,330,784,1660,3208,5763,9752,15724,24368,36520,53152,75392,
%T A341137 104464,141717,188624,246836,318088,404356,507656,630172,774048,
%U A341137 941685,1135304,1357652,1611240,1899138,2224016,2589352,2997544,3452619,3957480,4516912,5134096,5815338
%N A341137 Number of ways to write n as an ordered sum of 8 prime powers (including 1).
%p A341137 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341137 b:= proc(n, t) option remember;
%p A341137       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341137       `if`(q(j), b(n-j, t-1), 0), j=1..n)))
%p A341137     end:
%p A341137 a:= n-> b(n, 8):
%p A341137 seq(a(n), n=8..44);  # _Alois P. Heinz_, Feb 05 2021
%t A341137 nmax = 44; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &
%Y A341137 Cf. A000961, A010055, A282062, A282064, A341126, A341133, A341134, A341135, A341136, A341138, A341139.
%K A341137 nonn
%O A341137 8,2
%A A341137 _Ilya Gutkovskiy_, Feb 05 2021