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,. . . , 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,. . . , 1/n are integers. In this paper, we prove that if n ⩾ 5, then none of the elementary symmetric functions of 1, 1/2,. . . , 1/n\1/i are integers except for n = i = 2 and n = i = 4.
Zhang et al. (Wed,) studied this question.