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An Inequality on the Sum of Divisors

LE Mao-hua

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Abstract

For any positive integer k,let δ(k) denote the sum of distinct divisors of k,and let f(n)=δ(1)+δ(2)+…+δ(n).In this paper we prove that there exist infinitely many positive integers n satisfying δ(f(n))≥n(n+1).

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For any positive integer k,let δ(k) denote the sum of distinct divisors of k,and let f(n)=δ(1)+δ(2)+…+δ(n).In this paper we prove that there exist infinitely many positive integers n satisfying δ(f(n))≥n(n+1).

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Available abstract

For any positive integer k,let δ(k) denote the sum of distinct divisors of k,and let f(n)=δ(1)+δ(2)+…+δ(n).In this paper we prove that there exist infinitely many positive integers n satisfying δ(f(n))≥n(n+1).

Key concepts: Inequality, Mathematics, Mathematical economics, Combinatorics, Economics, Mathematical analysis

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