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

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

Offset

1,2

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.

Links

Table of n, a(n) for n=1..12.

José María Grau and Antonio M. Oller-Marcén, On k-Lehmer numbers, Integers, 12(2012), #A37.

Nathan McNew, Radically weakening the Lehmer and Carmichael conditions International Journal of Number Theory 9 (2013), 1215-1224.

Giovanni Resta, k-Lehmer numbers composite k-Lehmer numbers up to 10^12.

Example

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

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}]

Crossrefs

Cf. A187731, A173703, A234936.

Sequence in context: A277956 A307678 A151382 * A188675 A199876 A225029

Adjacent sequences: A234955 A234956 A234957 * A234959 A234960 A234961

Keyword

nonn

Author

Giovanni Resta, Jan 01 2014

Status

approved