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A231569 Composite numbers n such that lambda(n) divides 2n-2, where lambda is the Carmichael lambda function (A002322). 6

%I #33 Oct 27 2019 11:11:14

%S 4,6,8,12,15,24,28,66,91,276,435,532,561,616,703,946,1105,1128,1288,

%T 1729,1891,2465,2701,2821,2926,3367,5551,6601,8646,8695,8911,10585,

%U 11305,11476,12403,13981,15051,15841,16471,18721,19096,23001,26335,29341,30889

%N Composite numbers n such that lambda(n) divides 2n-2, where lambda is the Carmichael lambda function (A002322).

%C Contains the Carmichael numbers (A002997).

%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="/A231569/b231569.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[2 (# -1)/ CarmichaelLambda[#]] &]

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

%Y Cf. A002322, A002997, A231570, A231571, A231572, A231573.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Nov 11 2013

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Last modified August 5 20:30 EDT 2024. Contains 374956 sequences. (Running on oeis4.)