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On A theorem of Niven
- Source :
- Canadian Mathematical Bulletin. 17:109-110
- Publication Year :
- 1974
- Publisher :
- Canadian Mathematical Society, 1974.
-
Abstract
- In [3], Niven proved that for any positive integer k, the density of the set of positive integers n for which (n, (φ(n))≤k is zero (where φ is the Euler to tient function). In this paper, we prove a related result—namely if k and j are any positive integers, then the density of the set of positive integers n for which (n,σj(n))≤k is zero (where σj(n) is the sum of the jth powers of the positive divisors of n). We will borrow from Niven’s technique, but we must make some crucial modifications.
- Subjects :
- Algebra
General Mathematics
Mathematics
Subjects
Details
- ISSN :
- 14964287 and 00084395
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- Canadian Mathematical Bulletin
- Accession number :
- edsair.doi...........47d29e9b8988f9f640045cd649f31e39