

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



341, 561, 645, 18705, 2113665, 2882265, 81722145, 9234602385, 19154790699045, 43913624518905, 56123513337585, 162522591775545, 221776809518265, 3274782926266545, 4788772759754985
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 (base2)". 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: A001567 A178723 A210993 * A006970 A007324 A007011
Adjacent sequences: A328688 A328689 A328690 * A328692 A328693 A328694


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Oct 25 2019


STATUS

approved



