OFFSET

1,4

COMMENTS

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Additive with a(p^e) = A000005(e).

Sum_{k=1..n} a(n) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} f(1/p) = 0.51780076119050171903..., where f(x) = -x + (1-x) * Sum_{k>=1} x^k/(1-x^k). - Amiram Eldar, Sep 29 2023

EXAMPLE

8 has 3 (1+e)-divisors, 1, 2 and 8. Two of these divisors, 2 and 8 = 2^3 are prime powers. Therefore, a(8) = 2.

MATHEMATICA

f[p_, e_] := DivisorSigma[0, e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

PROG

(PARI) A349281(n) = vecsum(apply(e->numdiv(e), factor(n)[, 2])); \\ Antti Karttunen, Nov 13 2021

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Nov 13 2021

STATUS

approved