A340146 Möbius transform of A247074(x) = phi(x)/(Product_{primes p dividing x} gcd(p-1, x-1)).

1, 0, 0, 1, 0, 1, 0, 2, 2, 3, 0, 1, 0, 5, 1, 4, 0, 2, 0, 3, 2, 9, 0, 2, 4, 11, 6, -3, 0, 2, 0, 8, 4, 15, 5, 4, 0, 17, 5, 6, 0, 3, 0, 9, -1, 21, 0, 4, 6, 12, 7, -5, 0, 6, 9, 18, 8, 27, 0, 3, 0, 29, 4, 16, 2, -11, 0, 15, 10, -6, 0, 8, 0, 35, 4, -7, 14, 6, 0, 12, 18, 39, 0, 13, 3, 41, 13, 18, 0, 13, 1, 21, 14, 45, 17, 8

Offset: 1

Author

Antti Karttunen, Dec 29 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, A247074.

Cf. also A340143, A340144, A340145.

Programs

PARI

A247074(n) = { my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); }; \\ From A247074
A340146(n) = sumdiv(n,d,moebius(n/d)*A247074(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A247074(d).