A340090 Dirichlet inverse of A219428, n - phi(n) - 1.

-1, 0, 0, -1, 0, -3, 0, -3, -2, -5, 0, -7, 0, -7, -6, -8, 0, -11, 0, -11, -8, -11, 0, -21, -4, -13, -8, -15, 0, -21, 0, -21, -12, -17, -10, -36, 0, -19, -14, -33, 0, -29, 0, -23, -20, -23, 0, -63, -6, -29, -18, -27, 0, -47, -14, -45, -20, -29, 0, -85, 0, -31, -26, -55, -16, -45, 0, -35, -24, -45, 0, -123, 0, -37

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, A033987, A051953, A219428, A340094, A340140, A340197, A340198.

Programs

PARI

up_to = 2^14;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA219428(n) = (n - 1 - eulerphi(n));
v340090 = DirInverseCorrect(vector(up_to, n, A219428(n)));
A340090(n) = v340090[n];
\\ Or as:
A340090(n) = if(1==n, -1, sumdiv(n, d, if(dA219428(n/d)*A340090(d), 0)));

Formula

a(1) = -1, for n > 1, a(n) = Sum_{d|n, dA219428(n/d) * a(d).