# On some constrained partitions of $k$-multiperfect numbers

Let $$n$$ be a $$k$$ -multiperfect number. Do we know an upper bound for the number of partitions of $$n$$ whose all summands are at the same time multiples of $$k$$ and the sum of distinct divisors of $$n$$?

• Could you be a bit more precise regarding your question, @SylvainJulien? – Jose Arnaldo Bebita-Dris Jan 22 at 8:13