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A365489
The number of divisors of the smallest cube divisible by n.
2
1, 4, 4, 4, 4, 16, 4, 4, 4, 16, 4, 16, 4, 16, 16, 7, 4, 16, 4, 16, 16, 16, 4, 16, 4, 16, 4, 16, 4, 64, 4, 7, 16, 16, 16, 16, 4, 16, 16, 16, 4, 64, 4, 16, 16, 16, 4, 28, 4, 16, 16, 16, 4, 16, 16, 16, 16, 16, 4, 64, 4, 16, 16, 7, 16, 64, 4, 16, 16, 64, 4, 16, 4
OFFSET
1,2
COMMENTS
The number of divisors of the cube root of the smallest cube divisible by n, A019555(n), is A365488(n).
LINKS
FORMULA
a(n) = A000005(A053149(n)).
Multiplicative with a(p^e) = 3*ceiling(e/3) + 1.
Dirichlet g.f.: zeta(s) * zeta(3*s) * Product_{p prime} (1 + 3/p^s - 1/p^(3*s)).
MATHEMATICA
f[p_, e_] := 3*Ceiling[e/3] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> 3*((x-1)\3) + 4, factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 05 2023
STATUS
approved