A358347 - OEIS

A358347

a(n) is the sum of the unitary divisors of n that are squares.

1, 1, 1, 5, 1, 1, 1, 1, 10, 1, 1, 5, 1, 1, 1, 17, 1, 10, 1, 5, 1, 1, 1, 1, 26, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 50, 1, 1, 1, 1, 1, 1, 1, 5, 10, 1, 1, 17, 50, 26, 1, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 10, 65, 1, 1, 1, 5, 1, 1, 1, 10, 1, 1, 26, 5, 1, 1, 1, 17, 82, 1

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OFFSET

1,4

COMMENTS

The number of unitary divisors of n that are squares is A056624(n).

LINKS

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

FORMULA

a(n) >= 1 with equality if and only if n is an exponentially odd number (A268335).

Multiplicative with a(p^e) = p^e + 1 if e is even, and 1 otherwise.

a(n) = A034448(n)/A358346(n).

Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = zeta(3/2)/(3*zeta(5/2)) = 0.6491241554... .