M. Merca†
Abstract: 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 Eulers partition function p(n) and the sum of the positive divisors function (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 1s in all the partitions of n is derived in this context.
MSC: 05A17, 05A19, 11P81.
keywords: divisors, partitions
DOI 10.56082/annalsarscimath.2023.1-2.163
†mircea.merca@upb.ro Department of Mathematical Methods and Models, Fundamental Sciences Applied in Engineering Research Center, University Politehnica of Bucharest, RO-060042 Bucharest, Romania and Academy of Romanian Scientists, 050044, Bucharest, Romania
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
