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Aug 26, 2018 at 0:24 comment added Gerhard Paseman Similarly, use multiplicativity of tau to classify numbers whose tau value is a multiple of four versus those that aren't (at most one prime has to have a power that is odd, and is not 3 mod 4.). I think finding how tau distributes mod 4 may enlighten. Gerhard "It's Elementary, My Dear Joseph" Paseman, 2018.08.25.
Aug 26, 2018 at 0:18 comment added Gerhard Paseman The only numbers with an odd number of divisors are perfect squares. That you see them at all relates to a problem of Landau: are there infinitely many primes which are one more than a square. In your case, two away from a square. Gerhard "Not Often Off By One" Paseman, 2018.08.25.
Aug 26, 2018 at 0:07 history asked Joseph O'Rourke CC BY-SA 4.0