A076619 Least x>1 such that x^d == 1 (mod d) for each divisor d of n, for all nonsquarefree numbers n (cf. A013929).

3, 3, 4, 7, 3, 7, 11, 7, 6, 4, 15, 3, 7, 11, 23, 16, 7, 8, 11, 27, 7, 15, 31, 22, 3, 35, 7, 16, 39, 11, 4, 43, 23, 31, 47, 7, 15, 34, 11, 27, 7, 15, 59, 40, 31, 12, 63, 6, 43, 3, 67, 16, 35, 71, 7, 22, 75, 31, 39, 52, 79, 11, 7, 83, 43, 14, 58, 87, 36, 23, 31, 47, 95, 22, 7, 15, 67

Offset: 1

Author

Benoit Cloitre, Oct 22 2002

Keywords

• nonn

Comments

If n is squarefree (cf. A005117), then the least x>1 such that x^d == 1 (mod d) (for each divisor d of n) equals n+1.

Crossrefs

Cf. A013929, A076333, A076618 (sequence for all integers).

Programs

Mathematica

f[n_] := If[(r = Times @@ FactorInteger[n][[;; , 1]]) < n, r, 0]; Select[f /@ Range[200], # > 0 &] + 1 (* Amiram Eldar, Feb 11 2021 *)

PARI

lista(nn) = {for(n=1, nn, if (!issquarefree(n), print1(A076618(n), ", ");););} \\ Michel Marcus, Jul 13 2013

Formula

a(p^m) = p+1 for p prime and m>1.

a(n) = A076618(A013929(n)). - Michel Marcus, Jul 13 2013

a(n) = A076333(n) + 1. - Amiram Eldar, Feb 11 2021