cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

561, 62745, 576480525985, 1886616373665, 3193231538989185, 11947816523586945, 101817952350880305, 171800042106877185
Offset: 1

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Author

Amiram Eldar, Nov 13 2019

Keywords

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

Crossrefs

Cf. A000203, A002997, A004394, A328691.

Programs

  • 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

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.

Original entry on oeis.org

399, 6304359999, 408598269695, 517270926095, 20203946790335
Offset: 1

Views

Author

Amiram Eldar and Daniel Suteu, Aug 29 2022

Keywords

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
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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