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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 = 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 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: A355599 A086149 A344515 * A125870 A076439 A341658 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

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