A336656 Numbers k not divisible by 3 such that the multiplicative order of 3 modulo k is squarefree.

1, 2, 4, 7, 8, 11, 13, 14, 22, 23, 26, 28, 31, 43, 44, 46, 47, 49, 52, 56, 59, 61, 62, 67, 71, 77, 79, 83, 86, 88, 91, 92, 94, 98, 103, 104, 107, 118, 121, 122, 124, 131, 134, 139, 142, 143, 154, 157, 158, 161, 166, 167, 169, 172, 179, 182, 184, 188, 191, 196

Offset: 1

Author

Amiram Eldar, Jul 28 2020

Keywords

• nonn

Examples

			2 is a term since the multiplicative order of 3 modulo 2 is 1 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. A007734, A005117, A049149, A336654, A336655.

Programs

Mathematica

Select[Range[200], !Divisible[#, 3] && SquareFreeQ[MultiplicativeOrder[3, #]] &]

PARI

isok(k) = (k % 3) && issquarefree(znorder(Mod(3,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 (~ 0.51175) are constants (Pappalardi, 2003).