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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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