%I
%S 341,561,645,18705,2113665,2882265,81722145,9234602385,19154790699045,
%T 43913624518905,56123513337585,162522591775545,221776809518265,
%U 3274782926266545,4788772759754985
%N Poulet numbers (Fermat pseudoprimes to base 2) k that have an abundancy index sigma(k)/k that is larger than the abundancy index of all smaller Poulet numbers.
%C No more terms below 2^64.
%C The corresponding rounded values of sigma(k)/k are 1.126, 1.540, 1.637, 1.693, 1.708, 1.726, 1.800, 1.816, 1.821, 1.823, 1.845, 1.863, 1.903, 1.910, 1.944, ...
%C _Shyam Sunder Gupta_ asked: "Can you find the smallest abundant number which is also pseudoprime (base2)". If it exists it is a term of this sequence and it is larger than 2^64.
%C 3470207934739664512679701940114447720865 is a Fermat pseudoprime to base 2 that is also an abundant number.  _Daniel Suteu_, Nov 09 2019
%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/canyoufind.htm">Can You Find no. 49</a>, December 17, 2017.
%t pouletQ[n_] := CompositeQ[n] && PowerMod[2, n  1, n ] == 1; rm = 0; s={}; Do[If[!pouletQ[n], Continue[]]; r = DivisorSigma[1, n]/n; If[r > rm, rm = r; AppendTo[s, n]], {n, 1, 3*10^6}]; s
%Y Cf. A000203, A001567, A004394.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Oct 25 2019
