OFFSET
1,8
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) >= 1, with equality if and only if n is cubefree (A004709).
Multiplicative with a(p^e) = 1 if e <= 2 and (p^(e+1)-1)/(p-1) otherwise.
Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(3*s-3) + 1/p^(3*s-2) + 1/p^(3*s-1) - 1/p^(4*s-3) - 1/p^(4*s-2)).
MATHEMATICA
f[p_, e_] := If[e < 3, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(e[i] < 3, 1, (p[i]^(e[i]+1)-1)/(p[i]-1)))};
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 01 2023
STATUS
approved