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

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

Author

Brad Clardy, Dec 25 2014

Keywords

• nonn

Comments

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.

Links

• 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.

Crossrefs

Cf. A001567, A182490, A001567.

Programs

Magma

// 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;

Extensions

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

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