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Composite numbers n such that lambda(n) divides 4n-4, where lambda is the Carmichael lambda function (A002322).
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%I #20 Oct 27 2019 11:11:23

%S 4,6,8,10,12,15,16,20,24,28,30,40,48,52,60,66,70,80,85,91,112,120,130,

%T 176,190,208,232,240,276,280,286,364,370,435,451,496,520,532,561,616,

%U 703,742,910,946,976,1036,1105,1128,1288,1387,1456,1729,1770,1891

%N Composite numbers n such that lambda(n) divides 4n-4, where lambda is the Carmichael lambda function (A002322).

%C Contains the Carmichael numbers (A002997) and A231569.

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

%H Amiram Eldar, <a href="/A231571/b231571.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[4 (# -1)/ CarmichaelLambda[#]] &]

%o (PARI) is(n)=!isprime(n) && (4*n-4)%lcm(znstar(n)[2])==0 && n>1 \\ _Charles R Greathouse IV_, Nov 13 2013

%Y Cf. A002322, A231569, A231570, A231572, A231573.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Nov 11 2013