A NOTE ON A CLASSICAL CONNECTION BETWEEN PARTITIONS AND DIVISORS

In this note, we consider the number of k’s in all the partitions of n in order to provide a new proof of a classical identity involving Euler’s partition function p(n) and the sum of the positive divisors function a(n). New relations connecting classical functions of multiplicative number theory wi...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Annals. Series on mathematics and its applications Ročník 15; číslo 1-2; s. 163 - 174
Hlavný autor: Mercat, M.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: 2023
ISSN:2066-5997, 2066-6594
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:In this note, we consider the number of k’s in all the partitions of n in order to provide a new proof of a classical identity involving Euler’s partition function p(n) and the sum of the positive divisors function a(n). New relations connecting classical functions of multiplicative number theory with the partition function p(n) from additive number theory are introduced in this context. The fascinating feature of these relations is their common nature. A new identity for the number of 1’s in all the partitions of n is derived in this context.
ISSN:2066-5997
2066-6594
DOI:10.56082/annalsarscimath.2023.1-2.163