A369427 - OEIS

A369427

The number of unitary divisors of n that are squares of primes.

0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

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OFFSET

1,36

COMMENTS

The number of exponents in the prime factorization of n that are equal to 2.

LINKS

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

FORMULA

Additive with a(p^e) = 1 if e = 2, and 0 otherwise.

a(n) > 0 if and only if n is in A038109.

a(A061742(n)) = n, and a(k) < n for all k < A061742(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} (1/p^2 - 1/p^3) = A085548 - A085541 = 0.27748478074162196208... .