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MathGroup Archive 2012

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Integers that are the sum of 2 nonzero squares in exactly 2 ways

  • To: mathgroup at smc.vnet.net
  • Subject: [mg125678] Integers that are the sum of 2 nonzero squares in exactly 2 ways
  • From: Cisco Lane <travlorf at yahoo.com>
  • Date: Wed, 28 Mar 2012 04:59:02 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I've been looking at integers that are the sum of 2 nonzero squares in exactly 2 ways. The smallest example is 50 = 5^2+5^2=7^2+1^2. The first few terms are 50, 65, 85, 125, 130, 145, ....  This is given in OEIS as https://oeis.org/A025285

If I plot the pairs {1,50},{2,65},{3,85},... I get a more or less straight line with a slope of about 8.85... In other words, eventually, about one in 8.85 integers qualify.

I wonder if there is a theoretical value for this approximate number of 8.85...?



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