The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066500 Numbers k such that 5 divides phi(k). 9
 11, 22, 25, 31, 33, 41, 44, 50, 55, 61, 62, 66, 71, 75, 77, 82, 88, 93, 99, 100, 101, 110, 121, 122, 123, 124, 125, 131, 132, 142, 143, 150, 151, 154, 155, 164, 165, 175, 176, 181, 183, 186, 187, 191, 198, 200, 202, 205, 209, 211, 213, 217, 220, 225, 231, 241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Related to the equation x^5 == 1 (mod k): sequence gives values of k such there are solutions 1 < x < k of x^5 == 1 (mod k). If k is a term of this sequence, then G = is a non-abelian group of order 5k, where 1 < r < n and r^5 == 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 5^2 = 25 and all primes congruent to 1 mod 5 (A045453). Hence sequence gives all k such that k == 0 (mod A045453(n)) for some n > 1 or k == 0 (mod 25). EXAMPLE x^5 == 1 (mod 11) has solutions 1 < x < 11, namely {3,4,5,9}. MATHEMATICA Select[Range, Divisible[EulerPhi[#], 5] &] (* Amiram Eldar, May 23 2022 *) PROG (PARI) { n=0; for (m=1, 10^10, if (eulerphi(m)%5 == 0, write("b066500.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 18 2010 CROSSREFS Cf. A000010, A045453, A066498, A066499, A066501, A066502. Column k=3 of A277915. Sequence in context: A095779 A062055 A332516 * A234314 A258738 A160272 Adjacent sequences: A066497 A066498 A066499 * A066501 A066502 A066503 KEYWORD nonn AUTHOR Benoit Cloitre, Jan 04 2002 EXTENSIONS Simpler definition from Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 25 2003 Extended by Ray Chandler, Nov 06 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 29 07:51 EST 2023. Contains 367429 sequences. (Running on oeis4.)