A336655 Odd numbers k such that the multiplicative order of 2 modulo k is squarefree.

1, 3, 7, 9, 11, 21, 23, 31, 33, 43, 47, 49, 59, 63, 67, 69, 71, 77, 79, 83, 89, 93, 99, 103, 107, 121, 127, 129, 131, 139, 141, 147, 151, 161, 167, 177, 179, 191, 201, 207, 211, 213, 217, 223, 227, 231, 233, 237, 239, 249, 253, 263, 267, 279, 281, 283, 301, 307

Offset: 1

Author

Amiram Eldar, Jul 28 2020

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Francesco Pappalardi, Square free values of the order function, New York J. Math., Vol. 9 (2003), pp. 331-344.

Crossrefs

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

Programs

Mathematica

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

PARI

isok(k) = (k % 2) && issquarefree(znorder(Mod(2,k))); \\ Michel Marcus, Jul 29 2020

Formula

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).