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

0,2

Links

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

Formula

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

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 *)

Crossrefs

Row sums of A258119.

Cf. A002033, A215366, A360791.

Sequence in context: A173338 A054600 A077570 * A253444 A336821 A299488

Adjacent sequences: A360710 A360711 A360712 * A360714 A360715 A360716

Keyword

nonn

Author

Alois P. Heinz, Feb 21 2023

Status

approved