OFFSET
1,2
COMMENTS
By Zsigmondy's theorem, a(n) > 1 except for n = 1 or 6.
Conjectures: (1) For every n the highest unique prime factor is of the form kn+1. The values for k are in A097407. (2) For each composite n many factors of the form kn+1 occur intermittently but always singly in any cofactor pair. (3) For each prime n every factor is of the form kn+1.
A prime factor of 2^n-1 is called primitive if it does not divide 2^r-1 for any r<n, cf. A086251.
a(n) is the greatest prime such that the multiplicative order of 2 mod a(n) equals n, or a(n)=1 if no such prime exists. - Jianing Song, Oct 23 2019
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..1206
FORMULA
PROG
(PARI) isprimitive(p, n) = {for (r=1, n-1, if (((2^r-1) % p) == 0, return (0)); ); return (1); }
a(n) = {f = factor(2^n-1); forstep(i=#f~, 1, -1, if (isprimitive(f[i, 1], n), return (f[i, 1])); ); return (1); } \\ Michel Marcus, Jul 15 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Marco Matosic, Aug 16 2004
EXTENSIONS
More terms and better description from Vladeta Jovovic, Sep 03 2004
a(1) and a(6) changed from 0 to 1 by Jianing Song, Oct 23 2019
STATUS
approved