A053288 Cototient of 2^n - 1.

0, 1, 1, 7, 1, 27, 1, 127, 79, 423, 111, 2367, 1, 5799, 5767, 32767, 1, 122175, 1, 568575, 319039, 1553599, 178527, 10141695, 1154431, 22391463, 20750335, 135669759, 3044479, 539141823, 1, 2147483647, 1626398143, 5726972583, 1835106367, 42598088703, 616318399, 91627367079, 84561979327, 625809227775

Offset

1,4

Comments

Number of elements in GF(2^n) that do not have maximal order. a(n)=1 if n is the exponent of a Mersenne prime, the single element which is not a generator for these is the unit. - Joerg Arndt, Jul 05 2011

Links

Amiram Eldar, Table of n, a(n) for n = 1..1206 (terms 1..250 from G. C. Greubel)

Formula

a(n) = A051953(A000225(n)).

Mathematica

Table[2^n - 1 - EulerPhi[2^n - 1], {n, 1, 50}] (* G. C. Greubel, May 31 2018 *)

Prog

(PARI) a(n)={my(m=2^n-1); return(m-eulerphi(m)); }
vector(66, n, a(n)) /* Joerg Arndt, Jul 05 2011 */

Crossrefs

Cf. A000010, A000225, A051953.

Sequence in context: A147347 A183109 A082172 * A282917 A050301 A146996

Adjacent sequences: A053285 A053286 A053287 * A053289 A053290 A053291

Keyword

nonn

Author

Labos Elemer, Mar 03 2000

Status

approved