A360713 Sum of all prime encoded perfect partitions of n.

1, 2, 4, 14, 16, 70, 64, 280, 356, 850, 1024, 4630, 4096, 10738, 20820, 47264, 65536, 176712, 262144, 643214, 1129572, 2246994, 4194304, 9716880, 17011472, 34785250, 68859688, 139829626, 268435456, 560518826, 1073741824, 2192136576, 4335013860, 8679894658

Offset: 0

Author

Alois P. Heinz, Feb 21 2023

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3321

Crossrefs

Row sums of A258119.

Cf. A002033, A215366, A360791.

Programs

Maple

b:= proc(n, l) option remember; `if`(n=1,
      mul(ithprime(mul(l[j], j=1..i-1))^(l[i]-1), i=1..nops(l)),
      add(b(n/d, [l[], d]), d=numtheory[divisors](n) minus{1}))
    end:
a:= n-> b(n+1, []):
seq(a(n), n=0..33);

Mathematica

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}}]];
a[n_] := b[n + 1, {}];
Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Nov 21 2023, after Alois P. Heinz *)

Formula

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