A378445 a(n) is the number of divisors d of n such that A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

0, 1, 1, 2, 1, 3, 1, 3, 1, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 4, 2, 3, 1, 6, 1, 3, 2, 4, 1, 6, 1, 4, 2, 3, 2, 6, 1, 3, 2, 6, 1, 6, 1, 4, 3, 3, 1, 7, 1, 4, 2, 4, 1, 6, 2, 6, 2, 3, 1, 8, 1, 3, 3, 5, 2, 6, 1, 4, 2, 6, 1, 9, 1, 3, 3, 4, 2, 6, 1, 7, 2, 3, 1, 8, 2, 3, 2, 6, 1, 9, 2, 4, 2, 3, 2, 9, 1, 4, 3, 6, 1, 6, 1, 6, 4

Offset: 1

Author

Antti Karttunen, Nov 27 2024

Keywords

• nonn

Comments

Number of terms of A369003 that divide n.

Links

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

Crossrefs

Inverse Möbius transform of A377874.

Cf. A000005, A369003, A378444.

Cf. also A174273, A378443.

Programs

PARI

A377874(n) = { my(f=factor(n)); (numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1])))%2); };
A378445(n) = sumdiv(n,d,A377874(d));

Formula

a(n) = Sum_{d|n} A377874(d).

a(n) = A000005(n) - A378444(n).