

A066502


Numbers k such that 7 divides phi(k).


9



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
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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, yx^k = y^7 = 1, yxy^(1) = x^r> is a nonabelian 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


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000


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

Cf. A045465, A066498, A066499, A066500, A066501, A000010.
Column k=4 of A277915.
Sequence in context: A084163 A181622 A086149 * A125870 A076439 A168474
Adjacent sequences: A066499 A066500 A066501 * A066503 A066504 A066505


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Jan 04 2002


EXTENSIONS

Simpler definition from Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 25 2003


STATUS

approved



