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A253595 Least Carmichael number that is divisible by the n-th cyclic number A003277(n), or 0 if no such number exists.

%I A253595 #43 Apr 23 2024 08:29:14
%S A253595 561,1105,1729,561,1105,62745,561,1729,6601,2465,2821,561,825265,
%T A253595 29341,6601,334153,62745,561,2433601,74165065,29341,1105,8911,
%U A253595 116150434401,10024561,10585,41041,2508013,55462177,1105,11921001
%N A253595 Least Carmichael number that is divisible by the n-th cyclic number A003277(n), or 0 if no such number exists.
%C A253595 Has any odd cyclic number at least one Carmichael multiple?
%H A253595 Amiram Eldar, <a href="/A253595/b253595.txt">Table of n, a(n) for n = 3..2747</a> (calculated using data from Claude Goutier; terms 3..291 from Tim Johannes Ohrtmann, terms 292..853 from Max Alekseyev)
%H A253595 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 A253595 Gérard P. Michon, <a href="http://www.numericana.com/data/crump.htm">Carmichael Multiples of Odd Cyclic Numbers</a>.
%H A253595 Open Problem Garden, <a href="http://garden.irmacs.sfu.ca/?q=op/does_every_odd_number_coprime_to_its_euler_totient_divides_some_carmichael_number">Michon's conjecture</a>.
%H A253595 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%e A253595 a(8) = 62745 because this is the least Carmichael number which is divisible by 15 (the 8th cyclic number).
%o A253595 (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 A253595 isA002997(n)=n%2 && !isprime(n) && Korselt(n) && n>1
%o A253595 a(n) = {on = odd cyclic number(n); cn = 1; until (isA002997(cn) && (cn % on == 0), cn++); cn; }
%Y A253595 Cf. A002997, A003277, A135721.
%K A253595 nonn
%O A253595 3,1
%A A253595 _Tim Johannes Ohrtmann_, Jan 05 2015
%E A253595 a(292)-a(853) from _Max Alekseyev_, Apr 26 2015
%E A253595 Escape clause added by _Jianing Song_, Dec 12 2021