A101187 Values of m for which (6m+1)(12m+1)(18m+1) is a Carmichael number.

1, 5, 6, 11, 15, 22, 33, 35, 45, 51, 55, 56, 61, 85, 96, 100, 103, 105, 115, 121, 195, 206, 216, 225, 242, 255, 276, 370, 380, 426, 455, 470, 506, 510, 511, 550, 561, 588, 609, 628, 661, 700, 710, 741, 800, 805, 825, 871, 920, 930, 975, 1025, 1060, 1115, 1140

Offset: 1

Author

Gerard P. Michon, Dec 03 2004

Keywords

• nonn

Comments

A046025 is a subsequence giving the values of m for which the three factors are prime, which is a sufficient condition for the product (6m+1)(12m+1)(18m+1) to be a Carmichael number.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Bruno Berselli)
• Harvey Dubner, Carmichael Numbers of the form (6m+1)(12m+1)(18m+1), Journal of Integer Sequences, Vol. 5 (2002) Article 02.2.1.
• Gérard P. Michon, Generic Carmichael Numbers.

Crossrefs

Cf. A002997 (Carmichael numbers), A046025 (subsequence), A101186.

See also A065703.

Programs

Magma

[n: n in [1..1200] | IsOne(t mod CarmichaelLambda(t)) where t is (6*n+1)*(12*n+1)*(18*n+1)]; // Bruno Berselli, Jan 22 2013

Mathematica

CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 1200, CarmichaelNbrQ[(6# + 1)(12# + 1)(18# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)