[1] Cheng Linfeng*,. A Result on Multiply Perfect Number [J]. Journal of Southeast University (English Edition), 2002, 18 (3): 265-269. [doi:10.3969/j.issn.1003-7985.2002.03.014]
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A Result on Multiply Perfect Number(
)
关于多重完全数的一个结论
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 18
- Issue:
- 2002 3
- Page:
- 265-269
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2002-09-30
Info
- Title:
- A Result on Multiply Perfect Number
- 关于多重完全数的一个结论
- Author(s):
- Cheng Linfeng*
- Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
- 程林凤
- 中国矿业大学数学系, 徐州 221008
- Keywords:
- multiply perfect number; Euler theorem; divisible
- PACS:
- O516
- DOI:
- 10.3969/j.issn.1003-7985.2002.03.014
- Abstract:
- 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=23·3·5, 25·3·7, 25·33·5·7 satisfies σ(n)=ω(n)n(ω(n)≥3).
- 设n为大于1的正整数, ω(n)表示n的不同素因子的个数, σ(n)为n的所有正因子之和. 若σ(n)=2n, 则称n为完全数. 若σ(n)=kn(k≥3), 则称n为多重完全数. 本文以欧拉定理及费尔马定理为基础讨论了一种特定条件下的多重完全数问题, 即满足σ(n)=ω(n)·n(ω(n)≥3)的解的情况, 得到了σ(n)=ω(n)·n(ω(n)≥3)的全部解为n=23·3·5, 25·3·7, 25·33·5·7.
References:
[1] Birkhoff G D, Vangiver H S. On the integral divisors of an-bn[J].Ann Math, 1904, 5(2):173-180.
[2] Benito Franqui, Mariano Garcia.Some new multiply perfect numbers[J]. Amer Math Monthly, 1953, 60(3):459-462.
Memo
- Memo:
- * Born in 1967, female, graduate, lecturer.
Last Update: 2002-09-20