A340143 Möbius transform of A160595, where A160595(x) = phi(x)/gcd(phi(x), x-1).

1, 0, 0, 1, 0, 1, 0, 2, 2, 3, 0, 1, 0, 5, 3, 4, 0, 2, 0, 3, 2, 9, 0, 2, 4, 11, 6, -3, 0, 0, 0, 8, 4, 15, 11, 4, 0, 17, 11, 6, 0, 3, 0, 9, 0, 21, 0, 4, 6, 12, 15, -5, 0, 6, 19, 18, 8, 27, 0, 3, 0, 29, 13, 16, 2, -11, 0, 15, 10, -12, 0, 8, 0, 35, 12, -7, 14, 0, 0, 12, 18, 39, 0, 13, 15, 41, 27, 18, 0, 12, 3, 21, 14, 45, 35

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, A160595.

Cf. also A340141, A340142.

Programs

Mathematica

Table[DivisorSum[n, MoebiusMu[n/#1]*#2/GCD[#2, #3] & @@ {#, EulerPhi[#], # - 1} &], {n, 95}] (* Michael De Vlieger, Dec 29 2020 *)

PARI

A160595(n) = { my(x=eulerphi(n)); x/gcd(x,n-1); };
A340143(n) = sumdiv(n,d,moebius(n/d)*A160595(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A160595(d).