A234958 Number of composite k-Lehmer numbers up to 10^n.

0, 4, 19, 103, 422, 1559, 5645, 19329, 64040, 207637, 663845, 2103055

Offset: 1

Author

Giovanni Resta, Jan 01 2014

Keywords

• nonn
• more

Comments

A number n is a k-Lehmer number if there exist a k such that phi(n) divides (n-1)^k.

The values of a(10) and a(11) computed by N. McNew in the linked paper are smaller than mine. I provide a link to my full list so that it could be independently checked.

Examples

			There are 4 k-Lehmer numbers up to 10^2, namely 15, 51, 85, and 91, so a(2) = 4.
		

Links

• José María Grau and Antonio M. Oller-Marcén, On k-Lehmer numbers, arXiv:1012.2337 [math.NT], 2010-2012; Integers, 12(2012), #A37.
• Nathan McNew, Radically weakening the Lehmer and Carmichael conditions, arXiv:1210.2001 [math.NT], 2012; International Journal of Number Theory 9 (2013), 1215-1224.
• Giovanni Resta, k-Lehmer numbers composite k-Lehmer numbers up to 10^12.

Crossrefs

Cf. A187731, A173703, A234936.

Programs

Mathematica

kLQ[n_] := n > 1 && ! PrimeQ[n] && Mod[n-1, Times @@ First /@ FactorInteger@ EulerPhi@n] == 0; Table[Length@ Select[Range[2, 10^k], kLQ], {k, 6}]