A193461 Numbers n such that phi(n) divides 2*(n-1).

1, 2, 3, 4, 5, 6, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 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, 257, 263

Offset

1,2

Comments

This sequence contains all prime numbers. Only two composite numbers are known in this sequence: 4, 6.

No more composites below 10^10. - Charles R Greathouse IV, Aug 24 2011

Larger composite terms, if any, must be Carmichael numbers (A002997). - Ivan Neretin, Aug 30 2015

None of the 246683 Carmichael numbers < 10^16 are in the sequence. - Robert Israel, Sep 06 2015

Links

Table of n, a(n) for n=1..59.

Maple

with(numtheory): A193461:=n->`if`((2*(n-1) mod phi(n)) = 0, n, NULL): seq(A193461(n), n=1..300); # Wesley Ivan Hurt, Sep 05 2015

Mathematica

Union@Table[If[IntegerQ[2*(n-1)/EulerPhi[n]], n], {n, 300}]

Prog

(PARI) is(n)=(2*n-2)%eulerphi(n)==0 \\ Charles R Greathouse IV, Jun 14 2013
(Magma) [n: n in [1..300] | ((2*n-2) mod EulerPhi(n) eq 0)]; // Vincenzo Librandi, Sep 01 2015

Crossrefs

Cf. A002997.

Sequence in context: A045745 A054010 A051948 * A192587 A174323 A103539

Adjacent sequences: A193458 A193459 A193460 * A193462 A193463 A193464

Keyword

nonn

Author

José María Grau Ribas, Jul 26 2011

Status

approved