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 A033948 Numbers that have a primitive root (the multiplicative group modulo n is cyclic). 55
 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 22, 23, 25, 26, 27, 29, 31, 34, 37, 38, 41, 43, 46, 47, 49, 50, 53, 54, 58, 59, 61, 62, 67, 71, 73, 74, 79, 81, 82, 83, 86, 89, 94, 97, 98, 101, 103, 106, 107, 109, 113, 118, 121, 122, 125, 127, 131, 134, 137, 139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence consists of 1, 2, 4 and numbers of the form p^i and 2p^i, where p is an odd prime and i >= 1. Sequence gives values of n such that x^2 == 1 (mod n) has no solution with 12 are given when there are exactly two solutions for n*j+1 is a square, 0<=j m(n) <> 1, [\$1..139]); # Peter Luschny, May 25 2017 MATHEMATICA Join[{1}, Select[ Range, IntegerQ[ PrimitiveRoot[#]] &]] (* Jean-François Alcover, Sep 27 2011 *) Select[Range, EulerPhi[#] == CarmichaelLambda[#] &] (* T. D. Noe, Jun 04 2013 *) result = {}; Do[count = 0; Do[If[Mod[j^2, n] == 1, count++], {j, 2, n - 2}]; If[count == 0, AppendTo[result, n]], {n, 1, 200}]; result (* Richard R. Forberg, Mar 26 2016 *) result = {}; Do[count = 0; Do[ r = Sqrt[n*j + 1]; If[IntegerQ[r], count++], {j, 0, n}]; If[count == 2, AppendTo[result, n]], {n, 0, 200}]; result  (* missing{1, 2} Richard R. Forberg, Mar 26 2016 *) PROG (PARI) is(n)=if(n%2, isprimepower(n) || n==1, n==2 || n==4 || (isprimepower(n/2, &n) && n>2)) \\ Charles R Greathouse IV, Apr 16 2015 CROSSREFS Cf. A033949 (complement), A072209, A001783 (Gaussian products used in the V. Shevelev example). Cf. also A002322, A060594, A062373, A034380, A160377. Union of 1, 2, 4, A061345, A278568. Sequence in context: A048627 A152757 A062462 * A285514 A117730 A174328 Adjacent sequences:  A033945 A033946 A033947 * A033949 A033950 A033951 KEYWORD nonn AUTHOR Calculated by Jud McCranie, entered by N. J. A. Sloane. STATUS approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)