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%I #13 Jul 12 2024 10:17:55
%S 1,90,392448,411264,804384,871416,1284192,1935360,7456512,396168192,
%T 24193572480,43171285248,54585498240,63178786944,123570274464,
%U 730078562304,823442861592,1420069242240,2354025332736,2506251331584,3606011136000,3697798293504,9951618862080
%N Numbers n such that (n, sigma(n)) lies on the hyperbola y^2 - x^2 = m^2, for some natural number m, i.e., sigma(n)^2 - n^2 = m^2.
%e sigma(90)^2 - 90^2 = 234^2 - 90^2 = 216^2, so 90 is a term of the sequence.
%t Select[ Range[ 1, 10^6 ], IntegerQ[ Sqrt[ DivisorSigma[ 1, # ]^2 - #^2 ] ] & ]
%Y Cf. A066764.
%K nonn
%O 1,2
%A _Joseph L. Pe_, Jan 18 2002
%E a(7)-a(10) from _Sean A. Irvine_, Nov 06 2023
%E a(11)-a(23) from _Martin Ehrenstein_, Jul 12 2024