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

3,1

Comments

Has any odd cyclic number at least one Carmichael multiple?

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.

Example

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

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
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; }

Crossrefs

Cf. A002997, A003277, A135721.

Sequence in context: A141705 A135721 A290486 * A047713 A006971 A270698

Adjacent sequences: A253592 A253593 A253594 * A253596 A253597 A253598

Keyword

nonn,changed

Author

Tim Johannes Ohrtmann, Jan 05 2015

Extensions

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

Escape clause added by Jianing Song, Dec 12 2021

Status

approved