OFFSET
1,8
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 1 if and only if n is a cubefree number (A004709).
a(n) = n if and only if n is a cubefull number (A036966).
a(n) = n/A360539(n).
Multiplicative with a(p^e) = p^e if e >= 3, and 1 otherwise.
Dirichlet g.f.: zeta(s-1) * Product_{p prime} (1 - p^(1-s) + p^(-s) - p^(1-3*s) - p^(1-2*s) + p^(-2*s) + p^(3-3*s)).
MATHEMATICA
f[p_, e_] := If[e > 2, p^e, 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] > 2, f[i, 1]^f[i, 2], 1)); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Feb 11 2023
STATUS
approved