Abstract
An exhaustive search has yielded 236 amicable pairs of which the lesser number is smaller than108{10^8}, 57 pairs being new. It has also yielded 9 new sociable groups of order 10 or less, of which the lesser number is smaller than6.107{6.10^7}; the 9 sociable groups are all of order 4. The sequence of iterates of the functions(n)=σ(n)−ns(n) = \sigma (n) - nstarting with 276 has also been extended to 119 terms.
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