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A341126 Number of partitions of n into 8 prime powers (including 1).

%I A341126 #10 Feb 22 2022 03:35:53
%S A341126 1,1,2,3,5,6,10,13,19,23,32,38,51,60,77,90,113,128,158,179,215,240,
%T A341126 287,316,373,409,475,517,599,645,741,799,908,971,1104,1173,1326,1408,
%U A341126 1580,1670,1874,1967,2198,2310,2563,2680,2976,3097,3426,3566,3926,4070,4485
%N A341126 Number of partitions of n into 8 prime powers (including 1).
%p A341126 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341126 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341126       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341126       `if`(q(i), b(n-i, min(n-i, i), t-1), 0)))
%p A341126     end:
%p A341126 a:= n-> b(n$2, 8):
%p A341126 seq(a(n), n=8..60);  # _Alois P. Heinz_, Feb 05 2021
%t A341126 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341126 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341126      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341126      If[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341126 a[n_] := b[n, n, 8];
%t A341126 Table[a[n], {n, 8, 60}] (* _Jean-François Alcover_, Feb 22 2022, after _Alois P. Heinz *)
%Y A341126 Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341125, A341127.
%K A341126 nonn
%O A341126 8,3
%A A341126 _Ilya Gutkovskiy_, Feb 05 2021