形如N=π~α3^(2β)Q^(2β)的奇完全数

Some Results Concerning Odd Perfect Numbers of the Form N = π~α 3^(2β)Q^(2β)

设正整数N满足N=πα32βQ2β,这里(Q,π)=(Q,3)=1,Q=p1...pk,且p1,...,pk是相异的奇素数.本文证明了当β=9时,N不是奇完全数.

Let N be a nalural number, and N=π^α 3^2β Q^3β, where （Q, π）=（Q,3）=1,Q=p1…,pk, and p1,…,pk are distinet odd primes. In this paper, it is proved that if β=9, then Nis not an odd perfect number.