The aliquot constant

Details The aliquot constant The aliquot constant

2009-12-18

arxiv.org/abs/0912.3660v1

Mathematics

Number Theory

16 pages

Scientific paper

The average value of log s(n)/n taken over the first N even integers is shown to converge to a constant lambda when N tends to infinity; moreover, the value of this constant is approximated and proven to be less than 0. Here s(n) sums the divisors of n less than n. Thus the geometric mean of s(n)/n, the growth factor of the function s, in the long run tends to be less than 1. This could be interpreted as probabilistic evidence that aliquot sequences tend to remain bounded.

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