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We consider two multiplicative statistics on the set of integer partitions:the norm of a partition, which is the product of its parts, and the supernormof a partition, which is the product of the prime numbers $p_i$ indexed by itsparts $i$. We introduce and study new statistics that are sums of reciprocalsof supernorms on three statistical ensembles of partitions, labelled by theirsize $|\lambda|=n$, their perimeter equaling $n$, and their largest partequaling $n$. We show that the cumulative statistics of the reciprocalsupernorm for each of the three ensembles are asymptotic to $e^{\gamma} \log n$as $n \to \infty$.

Asymptotics of Reciprocal Supernorm Partition Statistics