OFFSET
1,4
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = e if e = 2 or e is odd, and e-1 otherwise.
a(n) >= 1, with equality if and only if n is squarefree (A005117).
a(n) <= A286324(n), with equality if and only if n equals the square of a squarefree number (A062503).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(2) * Product_{p prime} (1 + 1/p^3 - 1/p^4 + 1/p^5) = 1.87133814920590891161... .
MATHEMATICA
f[p_, e_] := If[e == 2 || OddQ[e], e, e -1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> if(x%2 || x == 2, x, x-1), factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 12 2023
STATUS
approved