Dividing a square into equal-area rectangles

How many ways are there to tile an $n\times n$ square with exactly $n$ rectangles, each of which has integer sides and area $n$?

The sequence $C(n)$ begins 1, 2, 2, 9, 2, 46, 2, 250, 37. Clearly $C(p) = 2$ for prime $p$. The value $C(8) = 250$ was provided to me by Sjoerd Visscher, but I cannot vouch for it personally, not having seen the details of his enumeration.

OEIS was no help.

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