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%I #9 Feb 22 2022 03:50:10
%S 1,0,1,1,2,1,2,3,5,5,6,7,10,10,13,16,19,21,26,30,34,37,44,52,58,66,73,
%T 85,94,106,115,136,146,165,178,204,215,248,263,298,318,356,372,426,
%U 443,494,520,585,603,681,702,781,815,906,929,1044,1071,1178,1223
%N Number of partitions of n into 8 distinct prime powers (including 1).
%p q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
%p b:= proc(n, i, t) option remember; `if`(n=0,
%p `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p `if`(q(i), b(n-i, min(n-i, i-1), t-1), 0)))
%p end:
%p a:= n-> b(n$2, 8):
%p seq(a(n), n=39..97); # _Alois P. Heinz_, Feb 05 2021
%t q[n_] := q[n] = Length[FactorInteger[n]] < 2;
%t b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t If[q[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t a[n_] := b[n, n, 8];
%t Table[a[n], {n, 39, 97}] (* _Jean-François Alcover_, Feb 22 2022, after _Alois P. Heinz_ *)
%Y Cf. A000961, A010055, A341126, A341132, A341137, A341140, A341141, A341142, A341143, A341144.
%K nonn
%O 39,5
%A _Ilya Gutkovskiy_, Feb 05 2021
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