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

1,10

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.

Prog

(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;

Crossrefs

Cf. A001567, A182490, A001567.

Sequence in context: A174102 A217521 A331925 * A294617 A320450 A100886

Adjacent sequences: A252940 A252941 A252942 * A252944 A252945 A252946

Keyword

nonn

Author

Brad Clardy, Dec 25 2014

Extensions

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

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

Status

approved