On the Diophantine Equation x~(d(n))+y~(φ(n))=z~(σ(n))

For any positive integer n,let d(n),φ(n) and σ(n) denote the divisor function,Euler's totient function and the sum of distinct divisors of n respectively.In this paper we prove that if n is a positive integer with square free,then the equation xd(n)+yφ(n)=zσ(n) has no positive integer solution(x,y,z) except when n=2 or n is an odd prime with n≡3(mod 4).