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A341143 Number of partitions of n into 6 distinct prime powers (including 1).

%I A341143 #10 Feb 22 2022 03:35:45
%S A341143 1,1,1,1,3,3,5,5,7,8,10,10,16,16,20,22,28,27,35,36,44,47,56,57,70,72,
%T A341143 81,89,102,105,122,128,140,151,167,175,197,208,223,241,259,272,296,
%U A341143 316,331,359,378,400,423,452,468,507,525,556,580,619,631,684,701,748
%N A341143 Number of partitions of n into 6 distinct prime powers (including 1).
%p A341143 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341143 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341143       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341143       `if`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341143     end:
%p A341143 a:= n-> b(n$2, 6):
%p A341143 seq(a(n), n=22..81);  # _Alois P. Heinz_, Feb 05 2021
%t A341143 q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t A341143 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341143      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341143      If[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341143 a[n_] := b[n, n, 6];
%t A341143 Table[a[n], {n, 22, 81}] (* _Jean-François Alcover_, Feb 22 2022, after _Alois P. Heinz_ *)
%Y A341143 Cf. A000961, A010055, A341124, A341132, A341135, A341140, A341141, A341142, A341144, A341145.
%K A341143 nonn
%O A341143 22,5
%A A341143 _Ilya Gutkovskiy_, Feb 05 2021