2 problems

For ternary partitions, let $\operatorname{num}_{\mathcal T}(n,x)$ denote the associated numerator. Define $t(n)\coloneq\operatorname{num}_{\mathcal T}(n,1)$ for $n\geq 0$, with…

Let $\operatorname{num}_{\mathcal T}(n,x)$ denote the numerator associated with partitions into powers of $3$, and let $v_3(M)$ be the exponent of $3$ in the positive integer $M$.…