A336654 Numbers k such that lambda(k) is squarefree, where lambda is the Carmichael lambda function (A002322).

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 18, 21, 22, 23, 24, 28, 31, 33, 36, 42, 43, 44, 46, 47, 49, 56, 59, 62, 63, 66, 67, 69, 71, 72, 77, 79, 83, 84, 86, 88, 92, 93, 94, 98, 99, 103, 107, 118, 121, 124, 126, 129, 131, 132, 134, 138, 139, 141, 142, 147, 154, 158, 161

Offset: 1

Author

Amiram Eldar, Jul 28 2020

Keywords

• nonn

Examples

			6 is a term since lambda(6) = 2 is squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Imre Kátai, Square-free values of the Carmichael function, Mathematica Pannonica, Vol. 16, No. 2 (2005), pp. 199-203.
• Francesco Pappalardi, Filip Saidak and Igor E. Shparlinski, Square-free values of the Carmichael function, Journal of Number Theory, Vol. 103, No. 1 (2003), pp. 122-131.

Crossrefs

Cf. A002322, A005117, A005596, A049149, A336655, A336656.

Programs

Mathematica

Select[Range[160], SquareFreeQ[CarmichaelLambda[#]] &]

Formula

The number of terms not exceeding x is (k + o(1)) * x/(log(x)^(1-a)), where a = 0.373955... is Artin's constant (A005596), and k = 0.80328... is another constant (Pappalardi et al., 2003).