OFFSET
1,2
LINKS
FORMULA
a(p^k) = p*(k + 1) where p is a prime and k > 0.
Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 + 2/p^(s-1) - 2/p^s - 1/p^(2*s-1) + 1/p^(2*s)). - Amiram Eldar, Sep 17 2023
EXAMPLE
a(12) = a(2^2*3) = 2*(2 + 1) * 3*(1 + 1) = 36.
MATHEMATICA
a[n_] := Times @@ (#[[1]] (#[[2]] + 1) & /@ FactorInteger[n]); a[1] = 1; Table[a[n], {n, 65}]
Table[DivisorSigma[0, n] Last[Select[Divisors[n], SquareFreeQ]], {n, 65}]
PROG
(PARI) a(n)={numdiv(n)*factorback(factorint(n)[, 1])} \\ Andrew Howroyd, Jul 24 2018
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Ilya Gutkovskiy, May 12 2018
STATUS
approved