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...
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| Veröffentlicht in: | Annals. Series on mathematics and its applications Jg. 15; H. 1-2; S. 163 - 174 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
2023
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| ISSN: | 2066-5997, 2066-6594 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 2066-5997 2066-6594 |
| DOI: | 10.56082/annalsarscimath.2023.1-2.163 |