A336655 - OEIS

%I #12 Jul 30 2020 01:57:31

%S 1,3,7,9,11,21,23,31,33,43,47,49,59,63,67,69,71,77,79,83,89,93,99,103,

%T 107,121,127,129,131,139,141,147,151,161,167,177,179,191,201,207,211,

%U 213,217,223,227,231,233,237,239,249,253,263,267,279,281,283,301,307

%N Odd numbers k such that the multiplicative order of 2 modulo k is squarefree.

%H Amiram Eldar, <a href="/A336655/b336655.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 (~ 0.46437) are constants (Pappalardi, 2003).

%e 3 is a term since the multiplicative order of 2 modulo 3 is 2 which is squarefree.

%t Select[2 * Range[160] - 1, SquareFreeQ[MultiplicativeOrder[2, #]] &]

%o (PARI) isok(k) = (k % 2) && issquarefree(znorder(Mod(2,k))); \\ _Michel Marcus_, Jul 29 2020

%Y Cf. A002326, A005117, A049149, A336654, A336656.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jul 28 2020