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
Keywords
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.
Programs
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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).