A340187 Dirichlet inverse of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

1, -1, -2, 0, -4, 3, -6, 0, 2, 7, -10, -1, -12, 11, 12, 0, -16, -5, -18, -3, 20, 19, -22, 0, 12, 23, -2, -7, -28, -29, -30, 0, 36, 31, 44, 4, -36, 35, 44, 0, -40, -49, -42, -9, -24, 43, -46, 0, 30, -33, 60, -13, -52, 7, 76, 4, 68, 55, -58, 23, -60, 59, -36, 0, 80, -93, -66, -15, 84, -119, -70, -1, -72, 71, -52, -19

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

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

Prog

(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(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
v340187 = DirInverse(vector(up_to, n, A063994(n)));
A340187(n) = v340187[n];

Crossrefs

Cf. A063994, A340188, A340189.

Cf. also A023900, A340142, A340145, A340190.

Sequence in context: A128263 A241384 A140254 * A204187 A095202 A343923

Adjacent sequences: A340184 A340185 A340186 * A340188 A340189 A340190

Keyword

sign

Author

Antti Karttunen, Dec 31 2020

Status

approved