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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). 0

%I

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

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

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

%H J. M. Grau and A. Oller-Marcén, <a href="http://arxiv.org/abs/1311.3522">On the congruence sum_{j=1}^{n-1} j^{k(n-1)} == -1 (mod n). k-strong Giuga and k-Carmichael numbers</a>, arXiv:1311.3522 [math.NT], 2013.

%t 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 *)

%Y Cf. A002322, A055553.

%K nonn,more

%O 1,1

%A _José María Grau Ribas_, Mar 02 2014

%E a(8)-a(10) from _Giovanni Resta_, Mar 03 2014

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Last modified April 3 01:31 EDT 2020. Contains 333195 sequences. (Running on oeis4.)