A066763 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.
15, 45, 70, 75, 135, 140, 225, 280, 350, 375, 377, 405, 490, 560, 627, 665, 675, 700, 980, 1120, 1125, 1215, 1400, 1750, 1875, 1881, 1960, 2025, 2240, 2450, 2800, 3325, 3375, 3430, 3500, 3645, 3655, 3920, 4480, 4655, 4900, 4901, 5600, 5625, 5643, 6075
Offset: 1
Keywords
Examples
15^2 + phi(15)^2 = 225 + 64 = 289 = 17^2, so 15 is a term of the sequence.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
Select[ Range[ 1, 10^4 ], IntegerQ[ Sqrt[ #^2 + EulerPhi[ # ]^2 ] ] & ]
-
PARI
isok(k) = { issquare(k^2 + eulerphi(k)^2) } \\ Harry J. Smith, Mar 23 2010