On the Elementary Symmetric Functions of $\{1,1/2,\dots,1/n\}\backslash\{1/i\}$

In 1946, P. Erdős and I. Niven proved that there are only finitely many positive integers $n$ for which one or more of the elementary symmetric functions of $1, 1 / 2$ , $\dots, 1 / n$ are integers. In 2012, Y. Chen and M. Tang proved that if $n ⩾ 4$ , then none of the elementary symmetric functions of $1, 1 / 2, \dots, 1 / n$ are integers. In this paper, we prove that if $n ⩾ 5$ , then none of the elementary symmetric functions of ${1, 1 / 2, \dots, 1 / n} \ {1 / i}$ are integers except for $n = i = 2$ and $n = i = 4$ .

On the Elementary Symmetric Functions of ${1, 1 / 2, \dots, 1 / n} \ {1 / i}$

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On the Elementary Symmetric Functions of ${1, 1 / 2, \dots, 1 / n} \ {1 / i}$

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On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}{1,1/2,…,1/n}\{1/i}

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On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}{1,1/2,…,1/n}\{1/i}

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On the Elementary Symmetric Functions of ${1, 1 / 2, \dots, 1 / n} \ {1 / i}$

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On the Elementary Symmetric Functions of ${1, 1 / 2, \dots, 1 / n} \ {1 / i}$

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