OFFSET
1,4
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = (p^(floor(e/p)+1) - 1)/(p - 1).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (A332653(p)/(p^(p-1)-1) - 1/(p*(p-1))) = 2.253624924813... .
MATHEMATICA
f[p_, e_] := (p^(Floor[e/p] + 1) - 1)/(p - 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~, (f[i, 1]^(1+f[i, 2] \ f[i, 1])-1)/(f[i, 1] - 1)); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 14 2023
STATUS
approved