A340188 Sum of A063994 and its Dirichlet inverse, where A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

2, 0, 0, 1, 0, 4, 0, 1, 4, 8, 0, 0, 0, 12, 16, 1, 0, -4, 0, -2, 24, 20, 0, 1, 16, 24, 0, -4, 0, -28, 0, 1, 40, 32, 48, 5, 0, 36, 48, 1, 0, -48, 0, -8, -16, 44, 0, 1, 36, -32, 64, -10, 0, 8, 80, 5, 72, 56, 0, 24, 0, 60, -32, 1, 96, -88, 0, -14, 88, -116, 0, 0, 0, 72, -48, -16, 120, -108, 0, 1, 4, 80, 0, 48, 128, 84, 112

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. A063994, A318828, A340187, A340189.

Cf. also A319340, A340191.

Programs

PARI

up_to = 65537;
A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA063994(n)));
A340187(n) = v340187[n];
A340188(n) = (A063994(n)+A340187(n));

Formula

a(n) = A063994(n) + A340187(n).

a(n) = A340189(n) - A318828(n).