亲和数的数值算法和数量估计

Numeric Algorithm and Magnitude Estimation of Amicable Numbers

总结了搜寻亲和数的分解算法和递推算法,计算出1 000亿内的亲和数3 261对,根据数值结果给出了在一定范围内亲和数的数量估计式,得出1018内的亲和数约为百万对。

This paper proposes the decomposition algorithm and recursive algorithm to search amicable numbers. 3 261 pairs of amicable numbers are searched out within 100 billion. The numerical estimated expression of amicable numbers in a certain range is obtained according to numeric results. There are approximately one million amicable numbers in 1018 range.