A064238 Values of m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,3.

6, 36, 210, 270, 306, 330, 336, 600, 726, 1170, 1236, 1296, 1530, 1656, 2220, 2280, 2556, 3036, 3060, 3066, 4260, 4446, 4800, 4950, 5226, 5580, 5850, 6150, 6360, 6690, 6840, 6966, 7620, 7680, 7686, 7866, 8016, 8166, 8190, 8286, 8520, 8526, 8646, 8940, 9090

Offset: 1

Author

N. J. A. Sloane, Sep 23 2001

Keywords

• nonn

Comments

am+1, bm+1, cm+1 are primes and am | (N-1), bm | (N-1), cm |(N-1).

All m's are multiples of 6 and m, 2m and 3m divide m(2m+1)(3m+1)-1 automatically.

References

• Harvey Dubner (harvey(AT)dubner.com), personal communication, Jun 27 2001.

Links

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

Crossrefs

Cf. A046025, A087788.

Programs

Maple

q:= n-> andmap(isprime, [6*j*n+1$j=1..3]):
map(x-> 6*x, select(q, [$1..2000]))[];  # Alois P. Heinz, Jun 25 2023

Mathematica

CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda[n]] == 1; Select[ Range@ 9000, PrimeQ[# + 1] && PrimeQ[2# + 1] && PrimeQ[3# + 1] && CarmichaelNbrQ[(# + 1)(2 # + 1)(3 # + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)

Formula

a(n) = 6 * A046025(n).

Extensions

Offset corrected by Amiram Eldar, Oct 16 2019