

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)).


3



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
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OFFSET

1,1


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


FORMULA

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


PROG

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


CROSSREFS

Cf. A009195, A072994.
Sequence in context: A029721 A224400 A132067 * A216603 A166730 A109944
Adjacent sequences: A072986 A072987 A072988 * A072990 A072991 A072992


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Aug 21 2002


STATUS

approved



