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%I #49 Apr 22 2024 13:43:37
%S 561,62745,656601,11921001,26719701,45318561,174352641,230996949,
%T 662086041,684106401,689880801,1534274841,1848112761,2176838049,
%U 3022354401,5860426881,6025532241,6097778961,7281824001,7397902401,10031651841,10054063041,10585115841
%N Carmichael numbers divisible by 3.
%C 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.
%C Subsequence of A008585 and of A205947.
%C 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.
%H Amiram Eldar, <a href="/A258801/b258801.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Claude Goutier; terms 1..426, below 10^16, based on Richard Pinch data, from Giovanni Resta)
%H Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.
%H Richard G. E. Pinch, <a href="http://www.s369624816.websitehome.co.uk/rgep/cartable.html">Tables relating to Carmichael numbers</a>.
%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%p select(t -> t mod numtheory:-lambda(t) = 1, [seq(6*k+3,k=1..10^6)]); # _Robert Israel_, Jul 12 2015
%t Cases[Range[555,10^6,6],n_/;Mod[n,CarmichaelLambda[n]]==1]
%o (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
%o is(n)=n%6==3 && Korselt(n) && n>9 \\ _Charles R Greathouse IV_, Jul 20 2015
%Y Cf. A002997 (Carmichael numbers), A205947 (Carmichael numbers not congruent to 1 modulo 6).
%Y Cf. A008585 (3*n).
%Y Cf. A045410 (primes not congruent to 1 modulo 6).
%K nonn,changed
%O 1,1
%A _Fred Patrick Doty_, Jun 10 2015
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