OFFSET
1,8
COMMENTS
First differs from A366145 at n = 27.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = 1 if e <= p, and a(p^e) = e+1 if e > p.
a(n) >= 1, with equality if and only if n is in A207481.
Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^s - 1/p^((p+2)*s-1) + 1/p^((p+1)*s) + 1/p^((p+1)*s-1)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + 1/((p-1)*p^(p-1))) = 1.58396891058853238595... .
MATHEMATICA
f[p_, e_] := If[e <= p, 1, e+1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] <= f[i, 1], 1, f[i, 2]+1)); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 21 2023
STATUS
approved