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A231570 Composite numbers n such that lambda(n) divides 3n-3, where lambda is the Carmichael lambda function (A002322). 4

%I #20 Oct 27 2019 11:11:35

%S 9,21,45,63,65,105,117,133,231,273,341,481,561,585,645,651,1001,1105,

%T 1281,1365,1541,1729,2465,2821,3201,3605,4033,4371,4641,4921,5461,

%U 5565,6305,6533,6601,7107,7161,8321,8911,10585,11041,12545,13333,13833,14981

%N Composite numbers n such that lambda(n) divides 3n-3, where lambda is the Carmichael lambda function (A002322).

%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="/A231570/b231570.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[3 (# -1)/ CarmichaelLambda[#]] &]

%o (PARI) is(n)=!isprime(n) && (3*n-3)%lcm(znstar(n)[2])==0 && n>1 \\ _Charles R Greathouse IV_, Nov 13 2013

%Y Cf. A002322, A231569, A231571, A231572, A231573.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Nov 11 2013

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