Congruences for an arithmetic function from 3-colored Frobenius partitions

Abstract

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

5 pages

References in corpus (1)

• Congruences for the Number of Cubic Partitions Derived from Modular Forms