Some results concerning exponential divisors

[摘要] If the natural numbernhas the canonical formp1a1p2a2…prarthend=p1b1p2b2…prbris said to be an exponential divisor ofnifbi|aifori=1,2,…,r. The sum of the exponential divisors ofnis denoted byσ(e)(n).nis said to be ane-perfect number ifσ(e)(n)=2n;(m;n)is said to be ane-amicable pair ifσ(e)(m)=m+n=σ(e)(n);n0,n1,n2,…is said to be ane-aliquot sequence ifni+1=σ(e)(ni)−ni. Among the results established in this paper are: the density of thee-perfect numbers is.0087; each of the first10,000,000e-aliquot sequences is bounded.

[学科分类] 数学（综合）