OFFSET
1,4
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = 1 + [e = p], where [] is the Iverson bracket.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (p-1)/p^(p+1)) = 1.153074089009... .
MATHEMATICA
f[p_, e_] := If[e == p, 2, 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], 2, 1)); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 14 2023
STATUS
approved