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 A328691 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. 1

%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 (base-2)". 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

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)