OFFSET
1,1
COMMENTS
Related to the equation x^7 == 1 (mod k): sequence gives values of k such there are solutions 1 < x < k of x^7 == 1 (mod k).
If k is a term of this sequence, then G = <x, y|x^k = y^7 = 1, yxy^(-1) = x^r> is a non-abelian group of order 7k, where 1 < r < n and r^7 == 1 (mod k). For example, G can be the subgroup of GL(2, Z_k) generated by x = {{1, 1}, {0, 1}} and y = {{r, 0}, {0, 1}}. - Jianing Song, Sep 17 2019
The asymptotic density of this sequence is 1 (Dressler, 1975). - Amiram Eldar, May 23 2022
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
Robert E. Dressler, A property of the phi and sigma_j functions, Compositio Mathematica, Vol. 31, No. 2 (1975), pp. 115-118.
FORMULA
EXAMPLE
x^7 == 1 (mod k) has solutions 1 < x < k for k = 29, 43, 49, ...
MATHEMATICA
Select[Range[500], Divisible[EulerPhi[#], 7]&] (* Harvey P. Dale, Apr 12 2012 *)
PROG
(PARI) { n=0; for (m=1, 10^10, if (eulerphi(m)%7 == 0, write("b066502.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 18 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 04 2002
EXTENSIONS
Simpler definition from Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 25 2003
STATUS
approved