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%I #16 Dec 19 2024 21:16:46
%S 15,45,70,75,135,140,225,280,350,375,377,405,490,560,627,665,675,700,
%T 980,1120,1125,1215,1400,1750,1875,1881,1960,2025,2240,2450,2800,3325,
%U 3375,3430,3500,3645,3655,3920,4480,4655,4900,4901,5600,5625,5643,6075
%N Numbers k such that (k, phi(k)) lies on a circle with integral radius centered at the origin, i.e., k^2 + phi(k)^2 is a square.
%H Harry J. Smith, <a href="/A066763/b066763.txt">Table of n, a(n) for n = 1..1000</a>
%e 15^2 + phi(15)^2 = 225 + 64 = 289 = 17^2, so 15 is a term of the sequence.
%t Select[ Range[ 1, 10^4 ], IntegerQ[ Sqrt[ #^2 + EulerPhi[ # ]^2 ] ] & ]
%o (PARI) isok(k) = { issquare(k^2 + eulerphi(k)^2) } \\ _Harry J. Smith_, Mar 23 2010
%Y Cf. A066764, A066782.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Jan 17 2002