Inequalities Related to the Unitary Analogue of Lehmer Problem

摘要

Observing that divides if is a prime, where is the well known Euler function, Lehmer has asked whether there is any composite number with this property. For this unsolved problem, partial answers were given by several researchers. Considering the unitary analogue of , Subbarao noted that divides , if is the power of a prime; and sought for integers other than prime powers which satisfy this condition. In this paper we improve two inequalities, established by Subbarao and Siva Rama Prasad [5], to be satisfied by for which divides . M.V. Subbarao and V. Siva Rama Prasad, Some analogues of a Lehmer problem on the totient function, Rocky Mountain Journal of Mathematics; Vol. 15, Number 2: Spring 1985, 609-619.