Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if ...Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if σ(n)=kn(k≥3) then n is said to be a multiply perfect number. In this paper according to Euler theorem and Fermat theorem, we discuss the result of σ(n)=ω(n)n and prove that only n=2 3·3·5, 2 5·3·7, 2 5·3 3·5·7 satisfies σ(n)= ω(n) n(ω(n)≥3). ...展开更多
文摘Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if σ(n)=kn(k≥3) then n is said to be a multiply perfect number. In this paper according to Euler theorem and Fermat theorem, we discuss the result of σ(n)=ω(n)n and prove that only n=2 3·3·5, 2 5·3·7, 2 5·3 3·5·7 satisfies σ(n)= ω(n) n(ω(n)≥3). ...
