A329460 Carmichael numbers k that have an abundancy index sigma(k)/k that is larger than the abundancy index of all smaller Carmichael numbers.

561, 62745, 576480525985, 1886616373665, 3193231538989185, 11947816523586945, 101817952350880305, 171800042106877185

Offset

1,1

Comments

The corresponding rounded values of sigma(k)/k are 1.540, 1.652, 1.665, 1.794, 1.794, 1.815, 1.816, 1.893, ...

Do abundant Carmichael numbers exist?

Abundant Carmichael numbers do exist. The prime factorization of such a number is: 5 * 7 * 13 * 17 * 19 * 23 * 37 * 59 * 67 * 73 * 83 * 89 * 97 * 109 * 163 * 193 * 199 * 233 * 257 * 349 * 353 * 397 * 433 * 523 * 739 * 929 * 1153 * 2593 * 2953 * 3169 * 5569 * 7873 * 9397 * 70849 * 313897. - Daniel Suteu, Aug 16 2020

a(9) > 10^22. - Amiram Eldar, Apr 20 2024

Links

Table of n, a(n) for n=1..8.

Mathematica

carmichaelQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; rm = 0; s={}; Do[If[!carmichaelQ[n], Continue[]]; r = DivisorSigma[1, n]/n; If[r > rm, AppendTo[s, n]; rm = r], {n, 2, 10^5}]; s

Crossrefs

Cf. A000203, A002997, A004394, A328691.

Sequence in context: A182090 A006931 A258801 * A097061 A290497 A258839

Adjacent sequences: A329457 A329458 A329459 * A329461 A329462 A329463

Keyword

nonn,more,changed

Author

Amiram Eldar, Nov 13 2019

Status

approved