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

1,2

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.

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).

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A200381 A050118 A081754 * A004436 A028237 A194463

Adjacent sequences: A336651 A336652 A336653 * A336655 A336656 A336657

Keyword

nonn

Author

Amiram Eldar, Jul 28 2020

Status

approved