Aliquot Sequence 3630 Ends After Reaching 100 Digits

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 smaller than 10,000; we have reached at leat 95 digits for all of them. In particu lar, 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 less than or equal 10⁶.

Keywords:

• Aliquot sequences
• sum of divisors
• perfect number
• amicable pair
• sociable numbers
• aliquot cycles