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A341147 Number of partitions of n into 10 distinct prime powers (including 1).

%I A341147 #9 Mar 01 2022 05:40:04
%S A341147 1,0,0,1,1,1,2,1,3,3,3,4,7,5,9,10,12,10,17,17,23,24,29,32,44,40,53,57,
%T A341147 71,71,91,90,113,117,141,148,181,181,217,231,268,276,327,340,397,412,
%U A341147 472,493,571,590,671,710,794,831,934,981,1094,1150,1271,1345,1484,1556,1706
%N A341147 Number of partitions of n into 10 distinct prime powers (including 1).
%p A341147 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341147 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341147       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341147       `if`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341147     end:
%p A341147 a:= n-> b(n$2, 10):
%p A341147 seq(a(n), n=63..125);  # _Alois P. Heinz_, Feb 05 2021
%t A341147 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341147 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341147      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341147      If[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341147 a[n_] := b[n, n, 10];
%t A341147 Table[a[n], {n, 63, 125}] (* _Jean-François Alcover_, Mar 01 2022, after _Alois P. Heinz_ *)
%Y A341147 Cf. A000961, A010055, A341131, A341132, A341139, A341140, A341141, A341142, A341143, A341144, A341145, A341146.
%K A341147 nonn
%O A341147 63,7
%A A341147 _Ilya Gutkovskiy_, Feb 05 2021