A360713 - OEIS

%I #24 Nov 21 2023 08:40:33

%S 1,2,4,14,16,70,64,280,356,850,1024,4630,4096,10738,20820,47264,65536,

%T 176712,262144,643214,1129572,2246994,4194304,9716880,17011472,

%U 34785250,68859688,139829626,268435456,560518826,1073741824,2192136576,4335013860,8679894658

%N Sum of all prime encoded perfect partitions of n.

%H Alois P. Heinz, <a href="/A360713/b360713.txt">Table of n, a(n) for n = 0..3321</a>

%F a(n) = Sum_{k=1..A002033(n)} A258119(n,k).

%p b:= proc(n, l) option remember; `if`(n=1,

%p       mul(ithprime(mul(l[j], j=1..i-1))^(l[i]-1), i=1..nops(l)),

%p       add(b(n/d, [l[], d]), d=numtheory[divisors](n) minus{1}))

%p     end:

%p a:= n-> b(n+1, []):

%p seq(a(n), n=0..33);

%t 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 a[n_] := b[n + 1, {}];

%t Table[a[n], {n, 0, 33}] (* _Jean-François Alcover_, Nov 21 2023, after _Alois P. Heinz_ *)

%Y Row sums of A258119.

%Y Cf. A002033, A215366, A360791.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 21 2023