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

%I #19 Mar 06 2023 07:59:57

%S 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,

%T 572,723,955,1344,1793,2399,3280,4228,5728,7738,10223,13895,18324,

%U 24437,33007,43850,58173,77938,104689,139195,187497,252020,337731,452631,606942

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

%C 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.

%H Daniel Suteu, <a href="/A252943/b252943.txt">Table of n, a(n) for n = 1..63</a>

%H Jan Feitsma and William F. Galway, <a href="http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html">Tables of pseudoprimes and related data</a>.

%H R. G. E. Pinch, <a href="http://s369624816.websitehome.co.uk/rgep/psp-13.gz">Pseudoprimes up to 10^13</a>.

%o (Magma)

%o // Fermat pseudoprimes that are not Carmichael numbers,

%o // count by power of two intervals

%o for i:= 1 to 20 do

%o isum:=0;

%o for n:= 2^i + 1 to 2^(i+1) - 1 by 2 do

%o if (IsOne(2^(n-1) mod n)

%o and not IsPrime(n)

%o and not n mod CarmichaelLambda(n) eq 1)

%o then isum:=isum+1;

%o end if;

%o end for;

%o i,isum;

%o end for;

%Y Cf. A001567, A182490, A001567.

%K nonn

%O 1,10

%A _Brad Clardy_, Dec 25 2014

%E a(21) from _Jon E. Schoenfield_, Dec 25 2014

%E a(22)-a(50) from _Daniel Suteu_, Mar 06 2023