A258801 Carmichael numbers divisible by 3.

561, 62745, 656601, 11921001, 26719701, 45318561, 174352641, 230996949, 662086041, 684106401, 689880801, 1534274841, 1848112761, 2176838049, 3022354401, 5860426881, 6025532241, 6097778961, 7281824001, 7397902401, 10031651841, 10054063041, 10585115841

Offset

1,1

Comments

Most Carmichael numbers are congruent to 1 modulo 6. Those that are not are observed to include numbers that are 5 modulo 6 as well as multiples of 3.

Subsequence of A008585 and of A205947.

No member of this sequence is divisible by any prime of the form 6k+1, hence all prime factors for this sequence are members of A045410.

Links

Amiram Eldar, Table of n, a(n) for n = 1..4276 (terms 1..426, below 10^16, based on Richard Pinch data, from Giovanni Resta)

Richard G. E. Pinch, Tables relating to Carmichael numbers.

Maple

select(t -> t mod numtheory:-lambda(t) = 1, [seq(6*k+3, k=1..10^6)]); # Robert Israel, Jul 12 2015

Mathematica

Cases[Range[555, 10^6, 6], n_/; Mod[n, CarmichaelLambda[n]]==1]

Prog

(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
is(n)=n%6==3 && Korselt(n) && n>9 \\ Charles R Greathouse IV, Jul 20 2015

Crossrefs

Cf. A002997 (Carmichael numbers), A205947 (Carmichael numbers not congruent to 1 modulo 6).

Cf. A008585 (3*n).

Cf. A045410 (primes not congruent to 1 modulo 6).

Sequence in context: A083736 A182090 A006931 * A329460 A097061 A290497

Adjacent sequences: A258798 A258799 A258800 * A258802 A258803 A258804

Keyword

nonn

Author

Fred Patrick Doty, Jun 10 2015

Status

approved