A340191 Difference between A063994 and its Möbius transform.

0, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 6, 5, 1, 1, 1, 1, 1, 7, 10, 1, 1, 4, 12, 2, 1, 1, 0, 1, 1, 11, 16, 9, 1, 1, 18, 13, 1, 1, -2, 1, 1, 4, 22, 1, 1, 6, 1, 17, 1, 1, 1, 13, 3, 19, 28, 1, 1, 1, 30, 4, 1, 15, -6, 1, 1, 23, -4, 1, 1, 1, 36, 4, 1, 15, -8, 1, 1, 2, 40, 1, 3, 19, 42, 29, 1, 1, 5, 17, 1, 31, 46, 21

Offset: 1

Author

Antti Karttunen, Dec 31 2020

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A008683, A063994, A340190.

Programs

PARI

A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
A340191(n) = -sumdiv(n,d,(dA063994(d));

Formula

a(n) = A063994(n) - A340190(n).

a(n) = -Sum_{d|n, dA008683(n/d) * A063994(d).