A393054 Number of divisors d of n such that d and A276086(n) are not coprime, where A276086 is the primorial base exp-function.

0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 0, 4, 0, 0, 5, 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 5, 0, 2, 0, 0, 5, 4, 0, 0, 6, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 4, 6, 0, 0, 0, 0, 7

Offset

1,9

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base.

Formula

a(n) = Sum_{d|n} [gcd(d,A276086(n)) > 1], where [ ] is the Iverson bracket.

a(n) = A000005(n) - A393053(n).

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A393054(n) = { my(x=A276086(n)); sumdiv(n, d, 1!=gcd(d, x)); };

Crossrefs

Cf. A000005, A276086, A393053.

Cf. also A393052.

Sequence in context: A328828 A276009 A328842 * A113302 A292946 A196078

Adjacent sequences: A393051 A393052 A393053 * A393055 A393056 A393057

Keyword

nonn,base,easy

Author

Antti Karttunen, Feb 04 2026

Status

approved