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%I #10 Feb 22 2022 03:35:49
%S 1,1,2,3,5,6,10,12,17,20,27,31,41,45,56,63,77,83,101,108,128,136,160,
%T 168,196,204,236,245,281,288,331,340,387,395,450,457,519,525,594,598,
%U 677,678,763,764,855,851,957,949,1062,1053,1177,1161,1300,1276,1425,1403,1564
%N Number of partitions of n into 6 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), t-1), 0)))
%p end:
%p a:= n-> b(n$2, 6):
%p seq(a(n), n=6..62); # _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], t - 1], 0]]];
%t a[n_] := b[n, n, 6];
%t Table[a[n], {n, 6, 62}] (* _Jean-François Alcover_, Feb 22 2022, after _Alois P. Heinz_ *)
%Y Cf. A000961, A010055, A071330, A341112, A341122, A341123, A341125, A341126, A341127.
%K nonn
%O 6,3
%A _Ilya Gutkovskiy_, Feb 05 2021
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