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A341131 Number of partitions of n into 10 prime powers (including 1).

%I A341131 #9 Feb 27 2022 09:51:28
%S A341131 1,1,2,3,5,6,10,13,19,24,34,41,56,67,87,105,134,156,196,228,278,320,
%T A341131 387,439,526,593,698,783,915,1014,1179,1304,1497,1648,1884,2058,2342,
%U A341131 2551,2882,3130,3524,3802,4266,4595,5125,5504,6124,6548,7263,7750,8558
%N A341131 Number of partitions of n into 10 prime powers (including 1).
%p A341131 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341131 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341131       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341131       `if`(q(i), b(n-i, min(n-i, i), t-1), 0)))
%p A341131     end:
%p A341131 a:= n-> b(n$2, 10):
%p A341131 seq(a(n), n=10..60);  # _Alois P. Heinz_, Feb 05 2021
%t A341131 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341131 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341131      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341131      If[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341131 a[n_] := b[n, n, 10];
%t A341131 Table[a[n], {n, 10, 60}] (* _Jean-François Alcover_, Feb 27 2022, after _Alois P. Heinz_ *)
%Y A341131 Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341125, A341126, A341127.
%K A341131 nonn
%O A341131 10,3
%A A341131 _Ilya Gutkovskiy_, Feb 05 2021