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A341139 Number of ways to write n as an ordered sum of 10 prime powers (including 1).

%I A341139 #5 Feb 05 2021 18:45:23
%S A341139 1,10,55,220,715,1992,4915,10990,22660,43660,79463,137830,229460,
%T A341139 368710,574410,870644,1287545,1862110,2639135,3672050,5024035,6768950,
%U A341139 8992340,11792070,15279450,19579514,24832415,31193900,38837085,47952400,58750125,71458860,86328885
%N A341139 Number of ways to write n as an ordered sum of 10 prime powers (including 1).
%p A341139 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341139 b:= proc(n, t) option remember;
%p A341139       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341139       `if`(q(j), b(n-j, t-1), 0), j=1..n)))
%p A341139     end:
%p A341139 a:= n-> b(n, 10):
%p A341139 seq(a(n), n=10..42);  # _Alois P. Heinz_, Feb 05 2021
%t A341139 nmax = 42; CoefficientList[Series[Sum[Boole[PrimePowerQ[k] || k == 1] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &
%Y A341139 Cf. A000961, A010055, A282062, A282064, A341131, A341133, A341134, A341135, A341136, A341137, A341138.
%K A341139 nonn
%O A341139 10,2
%A A341139 _Ilya Gutkovskiy_, Feb 05 2021