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%I #10 Sep 08 2021 21:14:26
%S 5,9,21,33,255,315,585,819,1365,3591
%N Numbers k such that (2^lambda(k) - 1)/k is prime, where lambda(k) is the Carmichael lambda function (A002322).
%C The corresponding primes are 3, 7, 3, 31, 257, 13, 7, 5, 3, 73, ...
%e 5 is in the sequence since lambda(5) = 4 and (2^4 - 1)/5 = 3 is prime.
%t aQ[n_] := PrimeQ[(2^CarmichaelLambda[n]-1)/n]; a={}; Do[If[aQ[k], AppendTo[a,k]], {k,1,4000,2}]; a
%o (PARI) isok(n) = (denominator(p=(2^lcm(znstar(n)[2])-1)/n)==1) && isprime(p); \\ _Michel Marcus_, Dec 29 2017
%Y Cf. A002322.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Dec 29 2017
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