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On repeated values of \(\sigma\) and multiperfect numbers. (English) Zbl 1378.11085

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
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