On 3- and 9-regular overpartitions modulo powers of 3

We show that certain sums of partition numbers are divisible by multiples of 2 and 3. For example, if $p(n)$ denotes the number of unrestricted partitions of a positive integer n (and $p(0)=1$ , $p(n)=0$ for $n<0$ ), then for all nonnegative integers m, $$ \begin{align*}\sum_{k=0}^\infty p(24m+23-\omega(-2k))+\sum_{k=1}^\infty p(24m+23-\omega(2k))\equiv 0~ (\text{mod}~144),\end{align*} $$ where $\omega (k)=k(3k+1)/2$ .

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On 3- and 9-regular overpartitions modulo powers of 3

Cited by 4 publications

References 0 publications

Congruences for $$[j, k]-$$overpartitions with even parts distinct

Congruences for $$[j, k]-$$overpartitions with even parts distinct

Ramanujan's theta functions and internal congruences modulo arbitrary powers of 3

Divisibility of Sums of Partition Numbers by Multiples of 2 and 3

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