On composite n dividing φ(n)‎ T(n)‎+2

Abstract EN

Let φ denote the Eular's Totitient .

For any positive integer n let τ(n) denote the number of its positive divisors .

If T is the set of all composite numbers n > 4 for which n divides φ(n) τ(n) + 2 , we prove that every nЄT has at least five distinct prime factors .

Our result improves that of Yong- Gao and Jin -Hui Fang [4] and of Subbarao [3] .The proofs presented in the paper entirely different from the earlier authors .