A072989 Numbers m>0 such that the number of solutions to x^m==1 (mod m), 1<=x<=m, is not equal to gcd(m, phi(m)).

20, 30, 40, 42, 52, 60, 66, 68, 70, 78, 80, 84, 90, 100, 102, 104, 110, 114, 116, 120, 126, 130, 132, 136, 138, 140, 148, 150, 154, 156, 160, 164, 168, 170, 171, 174, 180, 182, 186, 190, 198, 200, 204, 208, 210, 212, 220, 222, 228, 230, 232, 234, 238, 240

Offset: 1

Author

Benoit Cloitre, Aug 21 2002

Keywords

• easy
• nonn

Comments

Conjecture: limit of a(n)/n is zero.

This conjecture is certainly wrong as stated, because sequences "Numbers such that..." have lim a(n)/n >= 1 and a(n) > n for all indices following the first one for which this holds, as here: a(1) > 1. - M. F. Hasler, Feb 24 2014

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..220

Crossrefs

Cf. A009195, A072994.

Programs

PARI

isok(m) = sum(x=1, m, Mod(x, m)^m==1) != gcd(m, eulerphi(m)); \\ Michel Marcus, Feb 18 2021

Formula

Equals { m>0 | A009195(m) != A072994(m) }. - M. F. Hasler, Feb 23 2014