A182490 -id:A182490 - cp's OEIS frontend

A225005 Number of Carmichael numbers (A002997) less than 2^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 6, 9, 10, 15, 19, 23, 33, 45, 55, 69, 95, 130, 162, 214, 290, 375, 483, 656, 864, 1118, 1446, 1874, 2437, 3130, 4058, 5188, 6642, 8521, 11002, 14236, 18400, 23631, 30521, 39376, 50685, 65590, 84817, 109857, 141892, 183507, 237217, 307278, 398506, 517446, 672105, 873109, 1136472, 1479525, 1927138, 2513234, 3278553, 4279356

Offset: 1

Max Alekseyev, Apr 23 2013

nonn

Amiram Eldar, Table of n, a(n) for n = 1..73 (terms 65..69 added using A182490; terms 70..73 calculated using data from Claude Goutier)
Jan Feitsma, The pseudoprimes below 2^64 - statistics. [Wayback Machine link]
Jan Feitsma and William Galway, Tables of pseudoprimes and related data.
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.

Cf. A002997, A055553, A208276, A108797.

Partial sums of A182490.

A252943 Number of Fermat pseudoprimes to base 2 between 2^n and 2^(n+1) that are not Carmichael numbers.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 3, 5, 10, 12, 14, 21, 31, 41, 64, 100, 127, 165, 216, 288, 397, 572, 723, 955, 1344, 1793, 2399, 3280, 4228, 5728, 7738, 10223, 13895, 18324, 24437, 33007, 43850, 58173, 77938, 104689, 139195, 187497, 252020, 337731, 452631, 606942

Offset: 1

Brad Clardy, Dec 25 2014

nonn

This is a count, by power-of-two intervals, of the number of Fermat pseudoprimes that are not Carmichael numbers. A182490 contains the count of Carmichael numbers by power-of-two intervals.

Daniel Suteu, Table of n, a(n) for n = 1..63
Jan Feitsma and William F. Galway, Tables of pseudoprimes and related data.
R. G. E. Pinch, Pseudoprimes up to 10^13.

Cf. A001567, A182490, A001567.

// Fermat pseudoprimes that are not Carmichael numbers,
// count by power of two intervals
for i:= 1 to 20 do
  isum:=0;
  for n:= 2^i + 1 to 2^(i+1) - 1 by 2 do
     if (IsOne(2^(n-1) mod n)
           and not IsPrime(n)
           and not n mod CarmichaelLambda(n) eq 1)
           then isum:=isum+1;
     end if;
  end for;
  i,isum;
end for;

a(21) from Jon E. Schoenfield, Dec 25 2014

a(22)-a(50) from Daniel Suteu, Mar 06 2023

A242435 Number of terms of A182116 between 2^n and 2^(n+1).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 6, 2, 7, 8, 6, 12, 11, 21, 24, 27, 35, 45, 68, 86, 117, 176, 206, 260, 370, 457, 565, 750, 967, 1321, 1531, 1978, 2842, 3723, 4587, 5677, 8354, 10708, 13435, 17259, 23040, 31741, 40146, 48596, 66728, 92193, 112771, 149002, 209890

Offset: 1

Brad Clardy, May 14 2014

nonn

This was done with data on Carmichael numbers below 10^21 provided by R. G. E. Pinch, and special computational assistance from William Stein.

There are 16396564 Carmichael numbers below 2^69 but only 849752 have the property of A182116. It looks as though the ratio of Carmichael numbers of this type to normal Carmichael numbers converges to a value around 0.051.

Richard Pinch, Carmichael numbers up to 10^21

Cf. A002997, A182116, A182108, A182490.

cp's OEIS Frontend

A225005 Number of Carmichael numbers (A002997) less than 2^n.

Views

Author

Keywords

Links

Crossrefs

A252943 Number of Fermat pseudoprimes to base 2 between 2^n and 2^(n+1) that are not Carmichael numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Extensions

A242435 Number of terms of A182116 between 2^n and 2^(n+1).

Views

Author

Keywords

Comments

Links

Crossrefs