When (n^2)|A122537(n)

[Jonathan Post]

Regarding  A122537 and A122543 (A122537(n)/n), are A122537(1) = 1, A122537(2)
= 4, A122537(4) = 16, A122537(5) = 25, and A(10) = 100 the only values for
which (n^2)|A122537(n)? Equivalently, 1, 2, 4, 5, 10 the only n such that n|
A122543(n)?
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