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

Offset

1

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

(PARI) a(n) = {my(f = factor(n)); sum(i = 1, #f~, if(f[i, 1] == f[i, 2], 1, 0)); }

Crossrefs

Cf. A051674, A076265, A100717, A129251.

Similar sequences: A125070, A276935, A293439, A366074, A367512, A369070, A369427, A369428.

Sequence in context: A346459 A193243 A281302 * A340599 A160753 A328981

Adjacent sequences: A369423 A369424 A369425 * A369427 A369428 A369429

Keyword

nonn,easy

Author

Amiram Eldar, Jan 23 2024

Status

approved