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

Author

Fred Patrick Doty, Jun 10 2015

Keywords

• nonn

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..10000 (calculated using data from Claude Goutier; terms 1..426, below 10^16, based on Richard Pinch data, from Giovanni Resta)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Richard G. E. Pinch, Tables relating to Carmichael numbers.
• Index entries for sequences related to Carmichael numbers.

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).

Programs

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]

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