The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066500 Numbers k such that 5 divides phi(k). 8
 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 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 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}. 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 11:07 EST 2021. Contains 349419 sequences. (Running on oeis4.)