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A231572 Composite numbers n such that lambda(n) divides 5n-5, where lambda is the Carmichael lambda function (A002322). 4

%I

%S 25,33,165,217,325,385,561,793,825,1025,1045,1065,1105,1353,1525,1705,

%T 1729,2465,2665,2821,3565,4123,4681,5005,5185,5425,6601,6697,8029,

%U 8569,8911,9073,10585,11005,12025,12505,12801,13237,13741,14707,14725,14905,15457

%N Composite numbers n such that lambda(n) divides 5n-5, 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 Charles R Greathouse IV, <a href="/A231572/b231572.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[5 (# -1)/ CarmichaelLambda[#]] &]

%o (PARI) is(n)=!isprime(n) && (5*n-5)%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

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Last modified April 1 14:05 EDT 2020. Contains 333159 sequences. (Running on oeis4.)