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On the equation s(n)=[n/2]

LE Mao-hua

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Abstract

Let n be a positive integer. Let σ(n) denote the sum of distinct divisors of n, and let s(n)=σ(n)-n. In this paper we prove that if n≡5(mod 8), then s(n)≠[n/2], where [n/2] is the integral part of n/2.

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What this paper is about

Let n be a positive integer. Let σ(n) denote the sum of distinct divisors of n, and let s(n)=σ(n)-n. In this paper we prove that if n≡5(mod 8), then s(n)≠[n/2], where [n/2] is the integral part of n/2.

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Available abstract

Let n be a positive integer. Let σ(n) denote the sum of distinct divisors of n, and let s(n)=σ(n)-n. In this paper we prove that if n≡5(mod 8), then s(n)≠[n/2], where [n/2] is the integral part of n/2.

Key concepts: Integer (computer science), Mathematics, Combinatorics, Computer science, Programming language

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