A097605 Numbers n such that phi(n) divides n^2 - 1, where phi(n) (A000010) is number of positive integers <= n and coprime to n.

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 35, 37, 41, 43, 47, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 255, 257

Offset

1,2

Comments

All primes are in the sequence. 2 is the only even integer in the sequence.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

phi(35) = 24, 24 divides 35^2 -1 = 1224.

Mathematica

Select[ Range[ 262], Mod[ #^2 - 1, EulerPhi[ # ]] == 0 &] (* Robert G. Wilson v, Sep 01 2004 *)

Prog

(PARI) is(n)=(n^2-1)%eulerphi(n)==0 \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

Cf. A098271, A000010.

Sequence in context: A322833 A117287 A121615 * A143578 A187731 A182140

Adjacent sequences: A097602 A097603 A097604 * A097606 A097607 A097608

Keyword

nonn

Author

Leroy Quet, Aug 30 2004

Extensions

More terms from Robert G. Wilson v and John W. Layman, Sep 01 2004

Status

approved