InforLorV4, Hal, Checkpoint, bibRecord, 005A51

Aliquot Sequence 3630 Ends After Reaching 100 Digits

Identifieur interne : 005A51 ( Hal/Checkpoint ); précédent : 005A50; suivant : 005A52

Aliquot Sequence 3630 Ends After Reaching 100 Digits

Auteurs : Manuel Benito ; Wolfgang Creyaufmueller ; Juan Luis Varona ; Paul Zimmermann [France]

Source :

Experimental Mathematics [ 1058-6458 ] ; 2002.

RBID : Hal:inria-00101005

Descripteurs français

mix :
- aliquot cycles, aliquot sequences, amicable pair, cycle aliquote, nombre amical, nombre parfait, nombre social, perfect number, sociable numbers, somme des diviseurs, suite aliquote, sum of divisors.

Abstract

In this paper we present a new computational record: the aliquot sequence starting at $3630$ converges to~$1$ after reaching a hundred decimal digits. Also, we show the current status of all the aliquot sequences starting with a number under $10000$. In particular, we have reached at least $112$ digits for the so-called ``Lehmer five sequences'', and 101 digits for the ``Godwin twelve sequences''. Finally, we give a summary showing the number of aliquot sequences of unknown end starting with a number~$\le 10^6$.

Url:

https://hal.inria.fr/inria-00101005

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Le document en format XML

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Aliquot Sequence 3630 Ends After Reaching 100 Digits

Aliquot Sequence 3630 Ends After Reaching 100 Digits

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Abstract

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