OFFSET
1,2
COMMENTS
Number of ways to factor n into 2 kinds of 2, 3 kinds of 3, 5 kinds of 5, ... , p kinds of p.
FORMULA
If n = Product (p_j^k_j) then a(n) = Product (binomial(p_j + k_j - 1, k_j)).
MAPLE
a:= n-> mul(binomial(i[1]+i[2]-1, i[2]), i=ifactors(n)[2]):
seq(a(n), n=1..100); # Alois P. Heinz, Oct 26 2019
MATHEMATICA
a[n_] := Times @@ (Binomial[#[[1]] + #[[2]] - 1, #[[2]]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 75}]
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - X)^p)[n], ", ")) \\ Vaclav Kotesovec, Aug 22 2021
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Oct 26 2019
STATUS
approved