A340094 Dirichlet inverse of A062830, n - phi(n) + 1.

1, -2, -2, 1, -2, 3, -2, -1, 0, 1, -2, -1, -2, -1, 0, 0, -2, -1, -2, 3, -2, -5, -2, 1, -2, -7, -2, 7, -2, 9, -2, -1, -6, -11, -4, 4, -2, -13, -8, -3, -2, 17, -2, 15, 2, -17, -2, 1, -4, -3, -12, 19, -2, 3, -8, -7, -14, -23, -2, -11, -2, -25, 4, -1, -10, 33, -2, 27, -18, 17, -2, -3, -2, -31, -4, 31, -10, 41, -2, 5

Offset: 1

Author

Antti Karttunen, Jan 05 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000010, A051953, A062830, A340090.

Programs

PARI

up_to = 16384;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1])*sumdiv(n, d, if(dA062830(n) = 1+(n-eulerphi(n));
v340094 = DirInverseCorrect(vector(up_to, n, A062830(n)));
A340094(n) = v340094[n];
\\ Or as:
A340094(n) = if(1==n, 1, -sumdiv(n, d, if(dA062830(n/d)*A340094(d), 0)));

Formula

a(1) = 1, for n > 1, a(n) = -Sum_{d|n, dA062830(n/d) * a(d).