A381014 If n = Product (p_j^k_j) then a(n) = Sum partition(p_j^k_j).

0, 2, 3, 5, 7, 5, 15, 22, 30, 9, 56, 8, 101, 17, 10, 231, 297, 32, 490, 12, 18, 58, 1255, 25, 1958, 103, 3010, 20, 4565, 12, 6842, 8349, 59, 299, 22, 35, 21637, 492, 104, 29, 44583, 20, 63261, 61, 37, 1257, 124754, 234, 173525, 1960, 300, 106, 329931, 3012, 63, 37, 493, 4567, 831820, 15

Offset: 1

Author

Ilya Gutkovskiy, Apr 10 2025

Keywords

• nonn

Crossrefs

Cf. A000041, A008481.

Programs

Mathematica

Join[{0}, Table[Plus @@ (PartitionsP[#[[1]]^#[[2]]] & /@ FactorInteger[n]), {n, 2, 60}]]

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, numbpart(f[k,1]^f[k,2])); \\ Michel Marcus, Apr 17 2025

Formula

If n = Product (p_j^k_j) then a(n) = Sum A000041(p_j^k_j).