关于奇完全数的素因子

On Prime Factors of Odd Perfect Number

给出并证明了奇完全数素因子的某些特征.

In the paper,the following results have been proved:1) Suppose a=p^(α_1)_1p^(α_2)_2…p^(α_n)_n (n≥8) is an odd perfect number, there p_i is an odd prime, then ∑ni=11p_i-1-α_i+1p^(α_i+1)_i-1>12 and ∑ni=11p_i<1;2) Suppose a=p^(α_1)_1p^(α_2)_2…p^(α_n)_n (p_1<p_2<…<p_n) is an odd perfect number, there p_i is an odd prime,then p_1≤n.