A365492 - OEIS

A365492

The number of divisors of the smallest 4th power divisible by n.

1, 5, 5, 5, 5, 25, 5, 5, 5, 25, 5, 25, 5, 25, 25, 5, 5, 25, 5, 25, 25, 25, 5, 25, 5, 25, 5, 25, 5, 125, 5, 9, 25, 25, 25, 25, 5, 25, 25, 25, 5, 125, 5, 25, 25, 25, 5, 25, 5, 25, 25, 25, 5, 25, 25, 25, 25, 25, 5, 125, 5, 25, 25, 9, 25, 125, 5, 25, 25, 125, 5, 25

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OFFSET

1,2

COMMENTS

First differs from A082476 at n = 32.

The number of divisors of the 4th root of the smallest 4th power divisible by n, A053166(n), is A365491(n).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000005(A053167(n)).

Multiplicative with a(p^e) = 4*ceiling(e/4) + 1.

Dirichlet g.f.: zeta(s) * zeta(4*s) * Product_{p prime} (1 + 4/p^s - 1/p^(4*s)).