[seqfan] Sum( floor( k^2/n ), k=1..n)

[Charles Greathouse]

A014817 is defined as in the title. You can also sum in the opposite
direction:
a(n) = n^2 - sum_{m=1..n} floor(sqrt(n*m-1))

But neither of these are efficient, taking n calculations (exponential in
the length of n). Is there a better way to compute this sum (and the
related ones in A166387, A166375, and A165993)? I keep having images of
Dirichlet's hyperbola method but can't quite work out how to do it
efficiently here.

Maybe it's not hard and I'm just not looking at it right?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University