A369426 - OEIS

A369426

The number of unitary divisors of n that are of the form p^p, where p is a prime.

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

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OFFSET

LINKS

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

FORMULA

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

a(n) > 0 if and only if n is in A100717.

a(A076265(n)) = n, and a(k) < n for all k < A076265(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} (1/p^p - 1/p^(p+1)) = 0.14994839882703405849... .

MATHEMATICA

f[p_, e_] := If[e == p, 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

PROG