Bayless, Jonathan; Kinlaw, Paul On repeated values of \(\sigma\) and multiperfect numbers. (English) Zbl 1378.11085 J. Comb. Number Theory 7, No. 3, 177-189 (2015). Summary: We prove several results concerning repeated values of the sum of divisors function \(\sigma\) at consecutive or nearby integers. We determine explicit upper and lower bounds for the sum of reciprocal of \(n\) such that \(\sigma(n) = \sigma(n+1)\). We also compute the value of the sum of reciprocals of the multiperfect numbers (numbers \(n\) such that \(n |\sigma(n)\)). MSC: 11N25 Distribution of integers with specified multiplicative constraints Keywords:multiperfect numbers; sum of reciprocals PDFBibTeX XMLCite \textit{J. Bayless} and \textit{P. Kinlaw}, J. Comb. Number Theory 7, No. 3, 177--189 (2015; Zbl 1378.11085) Online Encyclopedia of Integer Sequences: Numbers k such that k and k+1 have same sum of divisors. Decimal expansion of the sum of the reciprocals of the multiply-perfect numbers.