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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).

%I A367320 #21 Apr 23 2024 08:29:18
%S A367320 561,1105,1729,29341,41041,63973,172081,825265,852841,1773289,5310721,
%T A367320 9890881,12945745,18162001,31146661,93869665,133205761,266003101,
%U A367320 417241045,496050841,509033161,1836304561,1932608161,2414829781,4579461601,9799928965,11624584621,12452890681
%N 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).
%H A367320 Amiram Eldar, <a href="/A367320/b367320.txt">Table of n, a(n) for n = 1..169</a> (terms below 10^22 calculated using data from Claude Goutier)
%H A367320 Amiram Eldar, <a href="/A367320/a367320_1.txt">Table of n, a(n), (a(n)-1)/A002322(a(n)) for n = 1..169</a>.
%H A367320 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 A367320 <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%t A367320 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]
%o A367320 (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, ", ")))));}
%Y A367320 Subsequence of A002997.
%Y A367320 Cf. A002322, A174590, A226216, A306414, A367319.
%K A367320 nonn
%O A367320 1,1
%A A367320 _Amiram Eldar_, Nov 14 2023