English

Congruences for an arithmetic function from 3-colored Frobenius partitions

Number Theory 2015-03-13 v3 Combinatorics

Abstract

Let a(n)a(n) defined by n=1a(n)qn:=n=11(1q3n)(1qn)3.\sum_{n=1}^{\infty}a(n)q^n := \prod_{n=1}^{\infty}\frac{1}{(1-q^{3n})(1-q^n)^3}. In this note, we prove that for every non-negative integer nn, a(15n+6) \equiv 0\pmod{5}, a(15n+12) \equiv 0\pmod{5}. As a corollary, we obtained some results of Ono

Keywords

Cite

@article{arxiv.1003.0509,
  title  = {Congruences for an arithmetic function from 3-colored Frobenius partitions},
  author = {Laizhong Song and Xinhua Xiong},
  journal= {arXiv preprint arXiv:1003.0509},
  year   = {2015}
}

Comments

5 pages

R2 v1 2026-06-21T14:52:44.296Z