If you install Math::Pari, try the function sigma($N,0). That computes the total number of divisors of $N. It requires factorization to compute, but Math::Pari has very fast factorization algorithms.

If N = (p1^a1)*(p2^a2)*...(pR^aR) then sigma(N,0) = (a1+1)*(a2+1)*...(aR + 1)

This number is usually very small, even for huge N.

If sigma($N,0) is reasonable, you can call divisors($N), which returns a list of all the divisors in order. A simple binary search will find the desired number.

This should be incredibly faster than brute-force countdown searches for large N.

In reply to Re^8: OT: Finding Factor Closest To Square Root by tall_man
in thread OT: Finding Factor Closest To Square Root by QM

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