A393051 Number of divisors d of n such that d and A276086(d) are coprime, where A276086 is the primorial base exp-function.

1, 2, 1, 3, 2, 3, 2, 4, 1, 3, 2, 5, 2, 4, 2, 5, 2, 4, 2, 4, 2, 4, 2, 7, 2, 4, 1, 6, 2, 5, 2, 6, 2, 4, 3, 7, 2, 4, 2, 5, 2, 5, 2, 6, 2, 4, 2, 9, 2, 3, 2, 6, 2, 5, 3, 7, 2, 4, 2, 8, 2, 4, 2, 7, 4, 6, 2, 6, 2, 5, 2, 10, 2, 4, 2, 6, 3, 6, 2, 6, 1, 4, 2, 8, 3, 4, 2, 8, 2, 7, 3, 6, 2, 4, 4, 11, 2, 4, 2, 4, 2, 6, 2, 8, 3

Offset

1,2

Comments

Number of nonzero terms of A324583 that divide n.

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} A356162(d).

a(n) = A000005(n) - A393052(n).

a(n) >= A322584(n).

Prog

(PARI)
A356162(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (1==m); };
A393051(n) = sumdiv(n, d, A356162(d));

Crossrefs

Inverse Möbius transform of A356162.

Cf. A000005, A324583, A393052.

Cf. also A322584, A393053.

Sequence in context: A237127 A262746 A007828 * A378117 A070804 A303429

Adjacent sequences: A393048 A393049 A393050 * A393052 A393053 A393054

Keyword

nonn,base,easy

Author

Antti Karttunen, Feb 04 2026

Status

approved