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A066502 Numbers k such that 7 divides phi(k). 10
29, 43, 49, 58, 71, 86, 87, 98, 113, 116, 127, 129, 142, 145, 147, 172, 174, 196, 197, 203, 211, 213, 215, 226, 232, 239, 245, 254, 258, 261, 281, 284, 290, 294, 301, 319, 337, 339, 343, 344, 348, 355, 377, 379, 381, 387, 392, 394, 406, 421, 422, 426, 430 (list; graph; refs; listen; history; text; internal format)
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
Robert E. Dressler, A property of the phi and sigma_j functions, Compositio Mathematica, Vol. 31, No. 2 (1975), pp. 115-118.
FORMULA
a(n) are the numbers generated by 7^2 = 49 and all primes congruent to 1 mod 7 (A045465). Hence sequence gives all k such that k == 0 (mod A045465(n)) for some n > 1 or k == 0 (mod 49).
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
Column k=4 of A277915.
Sequence in context: A355599 A086149 A344515 * A125870 A076439 A341658
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 04 2002
EXTENSIONS
Simpler definition from Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 25 2003
STATUS
approved

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Last modified February 21 10:51 EST 2024. Contains 370233 sequences. (Running on oeis4.)