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A360713 Sum of all prime encoded perfect partitions of n.

%I A360713 #24 Nov 21 2023 08:40:33
%S A360713 1,2,4,14,16,70,64,280,356,850,1024,4630,4096,10738,20820,47264,65536,
%T A360713 176712,262144,643214,1129572,2246994,4194304,9716880,17011472,
%U A360713 34785250,68859688,139829626,268435456,560518826,1073741824,2192136576,4335013860,8679894658
%N A360713 Sum of all prime encoded perfect partitions of n.
%H A360713 Alois P. Heinz, <a href="/A360713/b360713.txt">Table of n, a(n) for n = 0..3321</a>
%F A360713 a(n) = Sum_{k=1..A002033(n)} A258119(n,k).
%p A360713 b:= proc(n, l) option remember; `if`(n=1,
%p A360713       mul(ithprime(mul(l[j], j=1..i-1))^(l[i]-1), i=1..nops(l)),
%p A360713       add(b(n/d, [l[], d]), d=numtheory[divisors](n) minus{1}))
%p A360713     end:
%p A360713 a:= n-> b(n+1, []):
%p A360713 seq(a(n), n=0..33);
%t A360713 b[n_, l_] := b[n, l] = If[n == 1, Product[Prime[Product[l[[j]], {j, 1, i - 1}]]^(l[[i]] - 1), {i, 1, Length[l]}], Sum[b[n/d, Append[l, d]], {d, Divisors[n]~Complement~{1}}]];
%t A360713 a[n_] := b[n + 1, {}];
%t A360713 Table[a[n], {n, 0, 33}] (* _Jean-François Alcover_, Nov 21 2023, after _Alois P. Heinz_ *)
%Y A360713 Row sums of A258119.
%Y A360713 Cf. A002033, A215366, A360791.
%K A360713 nonn
%O A360713 0,2
%A A360713 _Alois P. Heinz_, Feb 21 2023