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

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, 173, 208, 254, 328, 428, 563, 693, 928, 1130, 1454, 1879, 2481, 3234, 4164, 5231, 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

Offset

1,10

Comments

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)).

Links

Amiram Eldar, Table of n, a(n) for n = 1..72 (calculated using data from Claude Goutier)

Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.

Richard Pinch, Carmichael numbers up to 10^21.

Prog

(Magma)
for i:= 1 to 25 do
icount:=0;
for k := 2^i +1 to 2^(i+1)-1 by 2 do
  if (not IsPrime(k) and (k mod CarmichaelLambda(k) eq 1)) then icount +:=1;
  end if;
end for;
i, icount;
end for;

Crossrefs

Cf. A002997.

Sequence in context: A044924 A057036 A069004 * A053274 A243926 A281013

Adjacent sequences: A182487 A182488 A182489 * A182491 A182492 A182493

Keyword

nonn

Author

Brad Clardy, May 02 2012

Extensions

Extended to a(50) by T. D. Noe, May 02 2012

Extended to a(68) with data from R. Pinch by Brad Clardy, May 18 2014

Status

approved