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

1,1

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

Table of n, a(n) for n=1..15.

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

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

Crossrefs

Cf. A000203, A001567, A004394.

Sequence in context: A178723 A210993 A346567 * A006970 A007011 A064907

Adjacent sequences: A328688 A328689 A328690 * A328692 A328693 A328694

Keyword

nonn,more

Author

Amiram Eldar, Oct 25 2019

Status

approved