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

561, 1105, 1729, 561, 1105, 62745, 561, 1729, 6601, 2465, 2821, 561, 825265, 29341, 6601, 334153, 62745, 561, 2433601, 74165065, 29341, 1105, 8911, 116150434401, 10024561, 10585, 41041, 2508013, 55462177, 1105, 11921001

Offset: 3

Author

Tim Johannes Ohrtmann, Jan 05 2015

Keywords

• nonn

Comments

Has any odd cyclic number at least one Carmichael multiple?

Examples

			a(8) = 62745 because this is the least Carmichael number which is divisible by 15 (the 8th cyclic number).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 3..2747 (calculated using data from Claude Goutier; terms 3..291 from Tim Johannes Ohrtmann, terms 292..853 from Max Alekseyev)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Gérard P. Michon, Carmichael Multiples of Odd Cyclic Numbers.
• Open Problem Garden, Michon's conjecture.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A002997, A003277, A135721.

Programs

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
isA002997(n)=n%2 && !isprime(n) && Korselt(n) && n>1
a(n) = {on = odd cyclic number(n); cn = 1; until (isA002997(cn) && (cn % on == 0), cn++); cn; }

Extensions

a(292)-a(853) from Max Alekseyev, Apr 26 2015

Escape clause added by Jianing Song, Dec 12 2021