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A341144 Number of partitions of n into 7 distinct prime powers (including 1).

%I A341144 #10 Feb 22 2022 03:40:20
%S A341144 1,1,1,1,2,3,3,4,6,8,8,10,12,15,16,22,23,29,30,37,40,50,50,63,68,79,
%T A341144 81,99,101,121,127,147,153,182,182,214,224,253,262,304,309,351,365,
%U A341144 405,421,477,485,541,563,614,634,706,719,791,823,888,919,1006,1029,1115,1164
%N A341144 Number of partitions of n into 7 distinct prime powers (including 1).
%p A341144 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341144 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341144       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341144       `if`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341144     end:
%p A341144 a:= n-> b(n$2, 7):
%p A341144 seq(a(n), n=30..90);  # _Alois P. Heinz_, Feb 05 2021
%t A341144 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341144 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341144      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341144      If[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341144 a[n_] := b[n, n, 7];
%t A341144 Table[a[n], {n, 30, 90}] (* _Jean-François Alcover_, Feb 22 2022, after _Alois P. Heinz_ *)
%Y A341144 Cf. A000961, A010055, A341125, A341132, A341136, A341140, A341141, A341142, A341143, A341145.
%K A341144 nonn
%O A341144 30,5
%A A341144 _Ilya Gutkovskiy_, Feb 05 2021