cp's OEIS Frontend

A182490 Number of Carmichael numbers between 2^n and 2^(n+1).

%I A182490 #38 Apr 21 2024 10:00:12
%S A182490 0,0,0,0,0,0,0,0,1,2,2,1,3,1,5,4,4,10,12,10,14,26,35,32,52,76,85,108,
%T A182490 173,208,254,328,428,563,693,928,1130,1454,1879,2481,3234,4164,5231,
%U A182490 6890,8855,11309,14905,19227,25040,32035,41615,53710,70061,91228,118940,154659,201004,263363,343053,447613,586096,765319,1000803,1311065,1716615,2253877,2956272,3879379
%N A182490 Number of Carmichael numbers between 2^n and 2^(n+1).
%C A182490 While there may be an infinite number of Carmichael numbers, the ratio of Carmichael composites to odd composites (A094812), when looked at as a function of the power-of-two interval, apparently approaches 0 as the interval number n increases. It is 0.00533333 for n=10 but decreases to 0.00009035 by n=18 and is 0.00000254 at n=26, and looks like it could be reasonably modeled by 1/(A + B*log(n) + C*(log(n))^2 + D*(log(n)^3)).
%H A182490 Amiram Eldar, <a href="/A182490/b182490.txt">Table of n, a(n) for n = 1..72</a> (calculated using data from Claude Goutier)
%H A182490 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 A182490 Richard Pinch, <a href="http://www.s369624816.websitehome.co.uk/rgep/rpub.html#82">Carmichael numbers up to 10^21</a>.
%o A182490 (Magma)
%o A182490 for i:= 1 to 25 do
%o A182490 icount:=0;
%o A182490 for k := 2^i +1 to 2^(i+1)-1 by 2 do
%o A182490   if (not IsPrime(k) and (k mod CarmichaelLambda(k) eq 1)) then icount +:=1;
%o A182490   end if;
%o A182490 end for;
%o A182490 i, icount;
%o A182490 end for;
%Y A182490 Cf. A002997.
%K A182490 nonn
%O A182490 1,10
%A A182490 _Brad Clardy_, May 02 2012
%E A182490 Extended to a(50) by _T. D. Noe_, May 02 2012
%E A182490 Extended to a(68) with data from R. Pinch by _Brad Clardy_, May 18 2014