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%I #12 Jul 29 2020 06:20:55
%S 1,2,4,7,8,11,13,14,22,23,26,28,31,43,44,46,47,49,52,56,59,61,62,67,
%T 71,77,79,83,86,88,91,92,94,98,103,104,107,118,121,122,124,131,134,
%U 139,142,143,154,157,158,161,166,167,169,172,179,182,184,188,191,196
%N Numbers k not divisible by 3 such that the multiplicative order of 3 modulo k is squarefree.
%H Amiram Eldar, <a href="/A336656/b336656.txt">Table of n, a(n) for n = 1..10000</a>
%H Francesco Pappalardi, <a href="https://www.emis.de/journals/NYJM/nyjm/NYJM/j/2003/9-17.html">Square free values of the order function</a>, New York J. Math., Vol. 9 (2003), pp. 331-344.
%F The number of terms not exceeding x is (a + o(1))* x * log(x)^(b-1), where a and b (~ 0.51175) are constants (Pappalardi, 2003).
%e 2 is a term since the multiplicative order of 3 modulo 2 is 1 which is squarefree.
%t Select[Range[200], !Divisible[#, 3] && SquareFreeQ[MultiplicativeOrder[3, #]] &]
%o (PARI) isok(k) = (k % 3) && issquarefree(znorder(Mod(3,k))); \\ _Michel Marcus_, Jul 29 2020
%Y Cf. A007734, A005117, A049149, A336654, A336655.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 28 2020
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