Document Zbl 0572.10007

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Résultats et conjectures sur les nombres pratiques. (Results and conjectures about practical numbers). (French) Zbl 0572.10007

C. R. Acad. Sci., Paris, Sér. I 299, 895-898 (1984).

A positive integer m is called practical if every integer smaller than \(\sigma\) (m) is a sum of distinct divisors of m. The author formulates 18 theorems and states 7 conjectures about practical numbers. The proofs will appear elsewhere.

Reviewer: W.Narkiewicz

Cited in 3 Reviews

Cited in 2 Documents

MSC:

11A25	Arithmetic functions; related numbers; inversion formulas
11B39	Fibonacci and Lucas numbers and polynomials and generalizations

Keywords:

density properties; arithmetic functions; arithmetic progressions; sum of distinct divisors; practical numbers

Citations:

Zbl 0544.10005

Cite Review PDF