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A341146 Number of partitions of n into 9 distinct prime powers (including 1).

%I A341146 #12 Feb 27 2022 09:51:22
%S A341146 1,0,1,0,1,2,2,1,4,4,5,5,8,7,11,11,16,16,21,20,30,30,36,40,51,53,63,
%T A341146 67,82,89,105,111,133,143,163,176,203,218,246,267,301,324,357,389,431,
%U A341146 471,512,555,607,660,710,773,835,906,969,1057,1124,1224,1298,1407,1494
%N A341146 Number of partitions of n into 9 distinct prime powers (including 1).
%H A341146 Alois P. Heinz, <a href="/A341146/b341146.txt">Table of n, a(n) for n = 50..5000</a>
%p A341146 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341146 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341146       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341146       `if`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341146     end:
%p A341146 a:= n-> b(n$2, 9):
%p A341146 seq(a(n), n=50..110);  # _Alois P. Heinz_, Feb 05 2021
%t A341146 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341146 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341146      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341146      If[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341146 a[n_] := b[n, n, 9];
%t A341146 Table[a[n], {n, 50, 110}] (* _Jean-François Alcover_, Feb 27 2022, after _Alois P. Heinz_ *)
%Y A341146 Cf. A000961, A010055, A341127, A341132, A341138, A341140, A341141, A341142, A341143, A341144, A341145, A341147.
%K A341146 nonn
%O A341146 50,6
%A A341146 _Ilya Gutkovskiy_, Feb 05 2021