A381013 If n = Product (p_j^k_j) then a(n) = Product partition(p_j^k_j).

1, 2, 3, 5, 7, 6, 15, 22, 30, 14, 56, 15, 101, 30, 21, 231, 297, 60, 490, 35, 45, 112, 1255, 66, 1958, 202, 3010, 75, 4565, 42, 6842, 8349, 168, 594, 105, 150, 21637, 980, 303, 154, 44583, 90, 63261, 280, 210, 2510, 124754, 693, 173525, 3916, 891, 505, 329931, 6020, 392, 330, 1470, 9130, 831820, 105

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Formula

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

Maple

a:= n-> mul(combinat[numbpart](i[1]^i[2]), i=ifactors(n)[2]):
seq(a(n), n=1..60);  # Alois P. Heinz, Apr 11 2025

Mathematica

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

Prog

(PARI) a(n) = my(f=factor(n)); prod(i=1, #f~, numbpart(f[i, 1]^f[i, 2])); \\ Michel Marcus, Apr 11 2025

Crossrefs

Cf. A000041, A000688.

Sequence in context: A353955 A318954 A296375 * A306923 A366856 A137750

Adjacent sequences: A381010 A381011 A381012 * A381014 A381015 A381016

Keyword

nonn,mult

Author

Ilya Gutkovskiy, Apr 10 2025

Status

approved