Journal of Integer Sequences, Vol. 27 (2024), Article 24.4.5

Arithmetic Identities for Some Analogs of the 5-Core Partition Function


Subhajit Bandyopadhyay and Nayandeep Deka Baruah
Department of Mathematical Sciences
Tezpur University
Napaam 784028
Assam
India

Abstract:

Recently, Gireesh, Ray, and Shivashankar studied an analog, $\overline{a}_t(n)$, of the $t$-core partition function, $c_t(n)$. In this paper, we study the function $\overline{a}_5(n)$ (A053723) in conjunction with $c_5(n)$ (A368490), as well as another analogous function $\overline{b}_5(n)$ (A368495). We also find several arithmetic identities for $\overline{a}_5(n)$ and $\overline{b}_5(n)$.

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(Concerned with sequences A053723 A368490 A368495.)

Received December 27 2023; revised versions received December 28 2023; April 6 2024. Published in Journal of Integer Sequences, April 6 2024.

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