تفاصيل الرسالة العلمية

The purpose of this thesis is to investigate properties of exponentially multiplicatively perfect numbers and some of their generalizations. For a natural number , we call a divisor an exponential divisor of if divides for all . By we denote the product of all divisors of and we denote the product of all exponential divisors of . A positive integer is called -multiplicatively perfect if and is -multiplicatively exponentially perfect if In this thesis we study - multiplicatively perfect and give description for some of these numbers. In particular, we introduced the concept of -super plus multiplicatively exponentially perfect number ( super -perfect). We list all super -perfect numbers up to then we provide with a criterion for some numbers to be super -perfect. Finally, we propose a problem to give a general description of these numbers