Number of partitions of n into parts not divisible by m

TL;DR

This paper presents a formula and an efficient method for calculating the number of partitions of a natural number n into parts that are not divisible by a given natural number m.

Contribution

The paper introduces a new formula enabling practical and efficient computation of such partitions, improving on previous methods.

Findings

Derived a new formula for partition counts

Developed an efficient computational method

Facilitated practical calculations for large n and m

Abstract

In this note, we obtain a formula which leads to a practical and efficient method to calculate the number of partitions of n into parts not divisible by m for given natural numbers n and m.