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

1,1

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Gérard P. Michon, Generic Carmichael Numbers.

Example

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

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 *)

Crossrefs

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

Sequence in context: A009470 A111991 A081136 * A019757 A021503 A025470

Adjacent sequences: A101185 A101186 A101187 * A101189 A101190 A101191

Keyword

nonn

Author

Gerard P. Michon, Dec 08 2004

Status

approved