A340142 Dirichlet inverse of A160595, where A160595(x) = phi(x)/gcd(phi(x), x-1).

1, -1, -1, -1, -1, 0, -1, -1, -2, -2, -1, 1, -1, -4, -2, -1, -1, 1, -1, 1, -1, -8, -1, 2, -4, -10, -4, 9, -1, 6, -1, -1, -3, -14, -10, 3, -1, -16, -10, 4, -1, 4, -1, 1, 5, -20, -1, 3, -6, -5, -14, 17, -1, 4, -18, -10, -7, -26, -1, 8, -1, -28, -9, -1, -1, 24, -1, 1, -9, 30, -1, 4, -1, -34, -5, 25, -13, 22, -1, 7, -8, -38, -1, -5

Offset

1,9

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Prog

(PARI)
up_to = 65537;
A160595(n) = { my(x=eulerphi(n)); x/gcd(x, n-1); };
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
v340142 = DirInverse(vector(up_to, n, A160595(n)));
A340142(n) = v340142[n];

Crossrefs

Cf. A160595.

Cf. also A340141, A340143.

Sequence in context: A340145 A104320 A350818 * A242618 A180264 A225200

Adjacent sequences: A340139 A340140 A340141 * A340143 A340144 A340145

Keyword

sign

Author

Antti Karttunen, Dec 29 2020

Status

approved