一类奇完全数的Euler因子

The Euler's Factors of a Kind of Odd Perfect Number

设n=pα32βQ2β是奇完全数,其中p是奇素数,且p≡α≡1(mod 4),(p,Q)=1=(3,Q)=1,p是n的Eu-ler因子.本文证明了:σ(m2)≥35pα,其中m2=32βQ2β,σ(m2)是m2的全部约数的和.

Let n=pα32βQ2β be an odd perfect number,where p is odd prime,p≡α≡1（mod 4）,（p,Q）=1=（3,Q）=1, p is the Euler＇ s factor of n. In the paper, it is shown that a σ（m^2）≥35pα,, where m^2 = 32βQ2β,σ（m2^） is the sum of distinct divisors of m^2.