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A341125 Number of partitions of n into 7 prime powers (including 1).

%I A341125 #10 Feb 22 2022 03:36:56
%S A341125 1,1,2,3,5,6,10,13,18,22,30,35,47,54,68,78,97,107,132,146,173,190,225,
%T A341125 242,285,305,352,377,434,456,525,553,627,659,748,778,881,916,1028,
%U A341125 1068,1197,1232,1381,1421,1578,1619,1801,1837,2041,2079,2296,2337,2583,2613
%N A341125 Number of partitions of n into 7 prime powers (including 1).
%p A341125 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341125 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341125       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341125       `if`(q(i), b(n-i, min(n-i, i), t-1), 0)))
%p A341125     end:
%p A341125 a:= n-> b(n$2, 7):
%p A341125 seq(a(n), n=7..60);  # _Alois P. Heinz_, Feb 05 2021
%t A341125 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341125 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341125      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341125      If[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341125 a[n_] := b[n, n, 7];
%t A341125 Table[a[n], {n, 7, 60}] (* _Jean-François Alcover_, Feb 22 2022, after _Alois P. Heinz_ *)
%Y A341125 Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341124, A341126, A341127.
%K A341125 nonn
%O A341125 7,3
%A A341125 _Ilya Gutkovskiy_, Feb 05 2021