A367320 Carmichael numbers k such that (k-1)/lambda(k) > (m-1)/lambda(m) for all Carmichael numbers m < k, where lambda is the Carmichael lambda function (A002322).

561, 1105, 1729, 29341, 41041, 63973, 172081, 825265, 852841, 1773289, 5310721, 9890881, 12945745, 18162001, 31146661, 93869665, 133205761, 266003101, 417241045, 496050841, 509033161, 1836304561, 1932608161, 2414829781, 4579461601, 9799928965, 11624584621, 12452890681

Offset: 1

Author

Amiram Eldar, Nov 14 2023

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..169 (terms below 10^22 calculated using data from Claude Goutier)
• Amiram Eldar, Table of n, a(n), (a(n)-1)/A002322(a(n)) for n = 1..169.
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Subsequence of A002997.

Cf. A002322, A174590, A226216, A306414, A367319.

Programs

Mathematica

seq[kmax_] := Module[{s = {}, r, rm = 0, lam}, Do[If[CompositeQ[k], lam = CarmichaelLambda[k]; If[Mod[k, lam] == 1, r = (k - 1)/lam; If[r > rm, rm = r; AppendTo[s, k]]]], {k, 9, kmax, 2}]; s]; seq[10^6]

PARI

lista(kmax) = {my(r, rm = 0, lam); forcomposite(k = 4, kmax, if(k % 2, lam = lcm(znstar(k)[2]); if(k % lam == 1, r = (k-1)/lam; if(r > rm, rm = r; print1(k, ", ")))));}