A291619 Composite numbers k such that 2^k == 1 (mod cototient(k)).

15, 143, 869, 16727, 17017, 26791, 31135, 32399, 36863, 57599, 58609, 63145, 65535, 106327, 124241, 137863, 176399, 186623, 206111, 416111, 435599, 546407, 571097, 788839, 1040399, 1065023, 1101047, 1240001, 1301189, 1665799, 2108303, 2617871, 2643503, 2713621, 3161413

Offset

1,1

Comments

Terms k such that cototient(k) is also a composite number are 17017, 63145, 65535, 137863, 5082041, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..371 (terms below 10^10)

Example

15 is a term because 15 - phi(15) = 7 divides 2^(3*5) - 1 = 7*31*151.

Mathematica

Select[Range[10^7], And[CompositeQ[#], PowerMod[2, #, # - EulerPhi@ #] == 1] &] (* Michael De Vlieger, Aug 31 2017 *)

Prog

(PARI) cototient(n) = n - eulerphi(n);
isok(n) = Mod(2, cototient(n))^n==1;
lista(nn) = forcomposite(n=4, nn, if(isok(n), print1(n, ", ")));

Crossrefs

Cf. A000225 (2^n-1), A051953 (cototient), A160599 (n % cototient(n) == 1).

Sequence in context: A235864 A177065 A173406 * A071700 A133126 A240158

Adjacent sequences: A291616 A291617 A291618 * A291620 A291621 A291622

Keyword

nonn

Author

Altug Alkan, Aug 28 2017

Status

approved