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%I #18 Feb 22 2021 09:16:31
%S 3,5,7,11,13,23,29,31,43,47,53,59,61,67,71,79,83,103,107,131,139,149,
%T 157,167,173,179,191,211,223,227,229,239,263,269,277,283,293,311,317,
%U 331,347,349,359,367,373,383,389,419,421,431
%N Primes of the form 2*s + 1, where s is a squarefree number (A005117).
%C For these odd primes delta(p) = A055034(n) = (p-1)/2 is squarefree, and therefore the (Abelian) multiplicative group Modd p (see a comment on A203571 for Modd n, not to be confused with mod n) is guaranteed to be cyclic. This is because the number of Abelian groups of order n (A000688) is 1 precisely for the squarefree numbers A005117. See also A210845. One can in fact prove that the multiplicative group Modd p is cyclic for all primes (the case p=2 is trivial). - _Wolfdieter Lang_, Sep 24 2012
%H Amiram Eldar, <a href="/A066651/b066651.txt">Table of n, a(n) for n = 1..10000</a>
%e a(13) = A000040(18) = 61 = 2*30+1 = 2*A005117(19)+1.
%t Select[2 * Select[Range[200], SquareFreeQ] + 1, PrimeQ] (* _Amiram Eldar_, Feb 22 2021 *)
%o (PARI) isok(p) = isprime(p) && (p>2) && issquarefree((p-1)/2); \\ _Michel Marcus_, Feb 22 2021
%Y Cf. A005385, A066652, A066653.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jan 10 2002
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