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- Title
A NOTE ON A CLASSICAL CONNECTION BETWEEN PARTITIONS AND DIVISORS.
- Authors
Merca, M.
- 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 Euler's partition function p(n) and the sum of the positive divisors function ρ(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.
- Subjects
PARTITION functions; NUMBER theory; DIVISOR theory; PARTITIONS (Mathematics)
- Publication
Annals: Series on Mathematics & its Applications, 2023, Vol 15, Issue 1/2, p163
- ISSN
2066-5997
- Publication type
Article
- DOI
10.56082/annalsarscimath.2023.1-2.163