Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  401.10057
Autor:  Erdös, Paul; Richmond, B.
Title:  On partitions of N into summands coprime to N. (In English)
Source:  Aequationes Math. 18, 178-186 (1978).
Review:  Let R(n) and R'(n) denote the number of partitions of n into summands and distinct summands respectively that are relatively prime to n. P.Erdös has shown [Ann. of Math., II. Ser. 43, 437-450 (1942; Zbl 061.07905)] that

log R(n) ~ \pi\sqrt{2/3}\phi ½(n),  log R'(n) ~ \pi\sqrt{2/3}\phi ½(n)

where \phi (n) denotes Euler's function. This paper obtains more explicit and precise results by applying the results of K. F.Roth and G.Szekeres [Quart. J. Math., Oxford II. Ser. 5, 241-259 (1954; Zbl 057.03902})] than obtained by B.Richmond [J. Number Theory 9, 525-534 (1977; Zbl 363.10032)].
Classif.:  * 11P81 Elementary theory of partitions
Keywords:  partitions; asymptotic formulas
Citations:  Zbl.061.079; Zbl.363.10032; Zbl.057.039

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