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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 19 15:40 EDT 2022. Contains 356229 sequences. (Running on oeis4.)