OFFSET
1,4
LINKS
FORMULA
If n = Product (p_j^k_j) then a(n) = Sum ordered partition(k_j).
Additive with a(p^e) = 2^(e-1).
EXAMPLE
a(72) = 6 because 72 = 2^3 * 3^2 and 2^(3 - 1) + 2^(2 - 1) = 6.
MAPLE
a:= n-> add(2^(i[2]-1), i=ifactors(n)[2]):
seq(a(n), n=1..100); # Alois P. Heinz, Oct 29 2019
MATHEMATICA
a[1] = 0; a[n_] := Plus @@ (2^(#[[2]] - 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 90}]
PROG
(PARI) a(n)={vecsum([2^(k-1) | k<-factor(n)[, 2]])} \\ Andrew Howroyd, Oct 29 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 29 2019
STATUS
approved