A340190 Möbius transform of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

1, 0, 1, 0, 3, -1, 5, 0, 0, -3, 9, 0, 11, -5, -1, 0, 15, 0, 17, 0, -3, -9, 21, 0, 0, -11, 0, 2, 27, 1, 29, 0, -7, -15, -5, 0, 35, -17, -9, 0, 39, 3, 41, 0, 4, -21, 45, 0, 0, 0, -13, 2, 51, 0, -9, -2, -15, -27, 57, 0, 59, -29, 0, 0, 1, 11, 65, 0, -19, 7, 69, 0, 71, -35, 0, 2, -11, 9, 77, 0, 0, -39, 81, -2, -3, -41, -25

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, A340191.

Cf. also A007431, A340143, A340146, A340192.

Programs

PARI

A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
A340190(n) = sumdiv(n,d,moebius(n/d)*A063994(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A063994(d).

a(n) = A063994(n) - A340191(n).