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.

341, 561, 645, 18705, 2113665, 2882265, 81722145, 9234602385, 19154790699045, 43913624518905, 56123513337585, 162522591775545, 221776809518265, 3274782926266545, 4788772759754985

Offset: 1

Author

Amiram Eldar, Oct 25 2019

Keywords

• nonn
• more

Comments

No more terms below 2^64.

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, ...

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.

3470207934739664512679701940114447720865 is a Fermat pseudoprime to base 2 that is also an abundant number. - Daniel Suteu, Nov 09 2019

Links

• Shyam Sunder Gupta, Can You Find no. 49, December 17, 2017.

Crossrefs

Cf. A000203, A001567, A004394.

Programs

Mathematica

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