On Repeated Values of σ and Multiperfect Numbers

摘要

We prove several results concerning repeated values of the sum-of-divisors function σ at consecutive or nearby integers. We determine explicit upper and lower bounds for the sum of reciprocals of n such that σ(n) = σ(n + 1). We also compute the value of the sum of reciprocals of the multiperfect numbers (numbers n such that n | σ(n)).