A231573 - OEIS

%I #15 Aug 29 2018 12:11:54

%S 4,6,8,9,12,14,15,18,21,24,28,35,36,39,42,45,56,63,65,66,72,76,84,91,

%T 105,117,126,133,153,168,186,195,231,247,252,259,273,276,315,341,344,

%U 396,435,455,481,504,532,561,585,616,645,651,671,703,804,819,861

%N Composite numbers n such that lambda(n) divides 6n-6, where lambda is the Carmichael lambda function (A002322).

%C Contains the Carmichael numbers, A231569 and A231570.

%C Conjecture: the relative asymptotic density of Carmichael numbers in this sequence exists, is positive and smaller than 1.

%H Charles R Greathouse IV, <a href="/A231573/b231573.txt">Table of n, a(n) for n = 1..10000</a>

%H J. M. Grau and Antonio Oller-Marcén, <a href="https://arxiv.org/abs/1103.3483">Generalizing Giuga's conjecture</a>, arXiv:1103.3483 [math.NT], 2011.

%t Select [1 + Range[100000], ! PrimeQ[#] && IntegerQ[6 (# -1)/ CarmichaelLambda[#]] &]

%o (PARI) is(n)=!isprime(n) && (6*n-6)%lcm(znstar(n)[2])==0 && n>1 \\ _Charles R Greathouse IV_, Nov 13 2013

%Y Cf. A231569-A231575, A002322.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Nov 11 2013