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A341141 Number of partitions of n into 4 distinct prime powers (including 1).

%I A341141 #9 Jul 13 2021 09:19:48
%S A341141 1,1,1,2,3,4,5,7,7,9,9,11,12,15,15,19,18,21,21,26,25,30,29,35,32,39,
%T A341141 37,45,43,52,50,58,54,62,61,71,66,75,74,81,78,89,85,96,93,102,99,110,
%U A341141 103,115,117,122,120,131,127,136,136,139,142,153,147,154,160,163,165,177,175
%N A341141 Number of partitions of n into 4 distinct prime powers (including 1).
%p A341141 q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p A341141 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341141       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341141       `if`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341141     end:
%p A341141 a:= n-> b(n$2, 4):
%p A341141 seq(a(n), n=10..76);  # _Alois P. Heinz_, Feb 05 2021
%t A341141 q[n_] := q[n] = PrimeNu[n] < 2;
%t A341141 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341141      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341141      If[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341141 a[n_] := b[n, n, 4];
%t A341141 Table[a[n], {n, 10, 76}] (* _Jean-François Alcover_, Jul 13 2021, after _Alois P. Heinz_ *)
%Y A341141 Cf. A000961, A010055, A341122, A341132, A341133, A341140, A341142, A341143, A341144, A341145.
%K A341141 nonn
%O A341141 10,4
%A A341141 _Ilya Gutkovskiy_, Feb 05 2021