A101188 Values of k for which (7*k+1)*(8*k+1)*(11*k+1) is a Carmichael number.

18, 216, 24966, 228246, 299790, 403806, 413046, 446310, 514686, 760470, 948966, 1019190, 1087566, 1355526, 1374006, 1471950, 1582830, 1715886, 2159406, 2266590, 2334966, 2589990, 2833926, 3652590, 3661830, 3720966, 3874350

Offset: 1

Author

Gerard P. Michon, Dec 08 2004

Keywords

• nonn

Comments

All values of n are even (since there are no even Carmichael numbers). Small values happen to be congruent to 18 modulo 66. This first fails for a(34)=5206142, which yields the Carmichael number 86921811895459937817345 = (3*5*29*83777)*41649137*57267563. Below this, only 4 values of n (18, 216, 299790 and 446310) correspond to Carmichael numbers with at least 4 prime factors. Other values of n must be of the form 1848k+942, with k given by A101186.

Examples

			a(1) = 18 corresponds to a 4-factor Carmichael number: 3664585 = 127 *(5*29) * 199.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Gérard P. Michon, Generic Carmichael Numbers.

Crossrefs

Cf. A002997 (Carmichael numbers), A101186, A101187.

Programs

Mathematica

CarmichaelNbrQ[n_] := ! PrimeQ[n] && Mod[n, CarmichaelLambda[n]] == 1; Select[ Range[4000000], CarmichaelNbrQ[(7# + 1)(8# + 1)(11# + 1)] &] (* Robert G. Wilson v, Aug 24 2012 *)