AN IMPROVEMENT OF AN INEQUALITY OF OCHEM AND RAO CONCERNING ODD PERFECT NUMBERS

摘要

Let (n) denote the total number of prime divisors of n (counting multiplicity) and let !(n) denote the number of distinct prime divisors of n. Various inequalities have been proved relating !(N) and (N) when N is an odd perfect number. We improve on these inequalities. In particular, we show that if (3, N) = 1, then (N) 8 3!(N) 7 3 , and if 3 | N then (N) 21 8 !(N) 39.8.