Maximal number of bases for which composite number is Fermat pseudoprime

[pedja]

According to the Wikipedia article a composite number n is a strong pseudoprime to at most one quarter of all bases below n .

Do Fermat pseudoprimes have some similar property ? Is it known what is the largest number of bases for which composite n , that is not Carmichael number is Fermat pseudoprime ?

 

[Joffan]

2701 does pretty well, at about 48% bases.

 

[Joffan]

Looks like it stays under 50% pseudoprime bases for non-Carmichaels. Typically for the close approaches to 50% there's another root of 1 (other than -1) which also takes almost half of the results. The multiples of the factors take a different value from the Fermat test of course.