OFFSET
1,4
COMMENTS
The corresponding sum of divisors of the powerful part of n is A295294.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 1 iff n is squarefree (A005117).
Multiplicative with a(p^e) = 1 if e = 1 and e+1 otherwise.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} ((p^3 - p^2 + 2*p - 1)/(p^2*(p - 1))) = 2.71098009471568319328... .
Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^s + 2/p^(2*s) - 1/p^(3*s)). - Amiram Eldar, Sep 09 2023
MATHEMATICA
f[p_, e_] := If[e == 1, 1, e + 1]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(e = factor(n)[, 2]); prod(i=1, #e, if(e[i] == 1, 1, e[i] + 1))};
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 08 2022
STATUS
approved