OFFSET
1,4
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = (p^e - 1)/(p-1) - 1.
Dirichlet g.f.: zeta(s) * zeta(s-1) * Product_{p prime} (1 + (2*p - p^s*(p+1))/p^(2*s)).
a(n) > 0 if and only if n is powerful (A001694).
a(n) <= n with equality only when n = 1.
a(p^2) = p for a prime p.
MATHEMATICA
f[p_, e_] := (p^e - 1)/(p-1) - 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]^f[i, 2] - 1)/(f[i, 1] - 1) - 1); }
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Aug 15 2023
STATUS
approved