Aliquot sequences with small starting values

TL;DR

This paper reports on the comprehensive computation of aliquot sequences starting from small values, analyzing their behavior until termination or reaching a large number, and documenting various statistics and interesting findings.

Contribution

It provides the first extensive computational analysis of aliquot sequences with starting values under one million, including new data, statistics, and records.

Findings

All sequences with starting values less than a million were computed.

Sequences terminate at 1, a cycle, or reach 100 decimal digits.

Numerous new statistics, curiosities, and records are reported.

Abstract

We describe the results of the computation of aliquot sequences with small starting values. In particular all sequences with starting values less than a million have been computed until either termination occurred (at 1 or a cycle), or an entry of 100 decimal digits was encountered. All dependencies were recorded, and numerous statistics, curiosities, and records are reported.