A076619 - OEIS

A076619

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

%I #21 Feb 11 2021 03:32:17

%S 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,

%T 39,11,4,43,23,31,47,7,15,34,11,27,7,15,59,40,31,12,63,6,43,3,67,16,

%U 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

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

%C 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.

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

%F a(n) = A076618(A013929(n)). - _Michel Marcus_, Jul 13 2013

%F a(n) = A076333(n) + 1. - _Amiram Eldar_, Feb 11 2021

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

%o (PARI) lista(nn) = {for(n=1, nn, if (!issquarefree(n), print1(A076618(n), ", ");););} \\ _Michel Marcus_, Jul 13 2013

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

%K nonn

%O 1,1

%A _Benoit Cloitre_, Oct 22 2002