Aliquot sequence 3630 ends after reach 100 digits. (English) Zbl 1116.11326

Summary: 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 smaller than \(10,000\); we have reached at least 95 digits for all of them. 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 list showing the number of aliquot sequences of unknown end starting with a number less than or equal \(10^6\).


11Y55 Calculation of integer sequences
11A25 Arithmetic functions; related numbers; inversion formulas
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[1] Boender H., Experimental Mathematics 5 pp 257– (1996) · Zbl 0882.11068
[2] Benito M., Math. Comp. 68 pp 389– (1999) · Zbl 0957.11060
[3] Cavallar S., Vances in Cryptology, Asiacrypt’99 (Berlin, 1999) pp 195– (1999)
[4] Creyaufmüller W., Primzahlfamih,, 3. ed. (2000)
[5] Daberkow M., J. Symbolic Comput. 24 pp 267– (1997) · Zbl 0886.11070
[6] Erdos P., Math. Comp. 30 pp 641– (1976)
[7] Guy R. K., Unsolved Problems in Number Theory,, 2. ed. (1994) · Zbl 0805.11001
[8] Guy R. K., Math. Comp. 29 pp 101– (1975)
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