A356821 Lucas-Carmichael numbers k that have an abundancy index sigma(k)/k that is larger than the abundancy indices of all smaller Lucas-Carmichael numbers.

399, 6304359999, 408598269695, 517270926095, 20203946790335

Offset: 1

Author

Amiram Eldar and Daniel Suteu, Aug 29 2022

Keywords

• nonn
• hard
• more

Comments

The rounded values of sigma(k)/k are 1.604, 1.612, 1.666, 1.706, 1.752, ...

The sequence includes the smallest abundant Lucas-Carmichael number, which is <= 1012591408428327888883952080728349448745451794025524955777432246705535.

Crossrefs

Cf. A000203, A004394, A006972.

Similar sequences: A328691, A329460.

Programs

Mathematica

lc = Import["https://oeis.org/A006972/b006972.txt", "Table"][[;; , 2]]; rm = 0; s = {}; Do[n = lc[[k]]; r = DivisorSigma[-1, n]; If[r > rm, AppendTo[s, n]; rm = r], {k, 1, Length[lc]}]; s

Extensions

a(5) from Martin Ehrenstein, Jul 30 2023