[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(
)
)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
- Author(s):
- Cheng Linfeng*
- Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
- 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).
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