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On an Open Problem of the Arithmatic Function δ(n)

LE Mao-hua

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Abstract

For any positive integer n,δ(n)denotes the sum of distinct divisors of n.ln this paper we prove that there exist infinitely many positive integers n satisfying δ(n)n+n1/2+n1/3+…+n1/k for any fixed positive integer k.

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For any positive integer n,δ(n)denotes the sum of distinct divisors of n.ln this paper we prove that there exist infinitely many positive integers n satisfying δ(n)n+n1/2+n1/3+…+n1/k for any fixed positive integer k.

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Available abstract

For any positive integer n,δ(n)denotes the sum of distinct divisors of n.ln this paper we prove that there exist infinitely many positive integers n satisfying δ(n)n+n1/2+n1/3+…+n1/k for any fixed positive integer k.

Key concepts: Integer (computer science), Mathematics, Combinatorics, Function (biology), Discrete mathematics, Computer science, Biology, Evolutionary biology

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