A231573 Composite numbers n such that lambda(n) divides 6n-6, where lambda is the Carmichael lambda function (A002322).

4, 6, 8, 9, 12, 14, 15, 18, 21, 24, 28, 35, 36, 39, 42, 45, 56, 63, 65, 66, 72, 76, 84, 91, 105, 117, 126, 133, 153, 168, 186, 195, 231, 247, 252, 259, 273, 276, 315, 341, 344, 396, 435, 455, 481, 504, 532, 561, 585, 616, 645, 651, 671, 703, 804, 819, 861

Offset: 1

Author

José María Grau Ribas, Nov 11 2013

Keywords

• nonn

Comments

Contains the Carmichael numbers, A231569 and A231570.

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• J. M. Grau and Antonio Oller-Marcén, Generalizing Giuga's conjecture, arXiv:1103.3483 [math.NT], 2011.

Crossrefs

Cf. A231569-A231575, A002322.

Programs

Mathematica

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

PARI

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