A232167 Number of composite integers k less than 10^n such that lambda(k) divides 2k-2, where lambda is the Carmichael lambda function (A002322).

3, 9, 16, 31, 68, 149, 314, 724, 1670, 4063

Offset: 1

Author

José María Grau Ribas, Mar 02 2014

Keywords

• nonn
• more

Comments

Conjecture: A055553(n)/a(n) has a limit strictly smaller than 1 as n tends to infinity.

Links

• J. M. Grau and A. Oller-Marcén, On the congruence sum_{j=1}^{n-1} j^{k(n-1)} == -1 (mod n). k-strong Giuga and k-Carmichael numbers, arXiv:1311.3522 [math.NT], 2013.

Crossrefs

Cf. A002322, A055553.

Programs

Mathematica

For[k = 4; cnt = 0, True, k++, If[CompositeQ[k] && Divisible[2k-2, CarmichaelLambda[k]], cnt++]; If[IntegerQ[n = Log[10, k+1]], Print[n, " ", cnt]]]; (* Jean-François Alcover, Feb 16 2019 *)

Extensions

a(8)-a(10) from Giovanni Resta, Mar 03 2014