AN UPPER BOUND FOR THE NUMBER OF ODD MULTIPERFECT NUMBERS

作者：Yuan, Pingzhi^*

来源：Bulletin of the Australian Mathematical Society, 2014, 89(1): 1-4.

DOI：10.1017/S000497271200113X

• odd perfect numbers
• k-perfect numbers

A natural number n is called k-perfect if sigma(n) = kn. In this paper, we show that for any integers r >= 2 and k >= 2, the number of odd k-perfect numbers n with omega(n) <= r is bounded by (left perpendicular4(r)log(3)2right perpendicular+r(r)) Sigma(r)(i=1) (left perpendicularkr/2right perpendicular (i)), which is less than 4(r2) when r is large enough.

• 出版日期2014-2
• 单位华南师范大学