

A258801


Carmichael numbers divisible by 3.


6



561, 62745, 656601, 11921001, 26719701, 45318561, 174352641, 230996949, 662086041, 684106401, 689880801, 1534274841, 1848112761, 2176838049, 3022354401, 5860426881, 6025532241, 6097778961, 7281824001, 7397902401, 10031651841, 10054063041, 10585115841
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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(n1)%(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



