A066763 Numbers n such that (n, phi(n)) lies on a circle with integral radius centered at the origin, i.e., n^2 + phi(n)^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

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

15^2 + phi(15)^2 = 225 + 64 = 289 = 17^2, so 15 is a term of the sequence.

Mathematica

Select[ Range[ 1, 10^4 ], IntegerQ[ Sqrt[ #^2 + EulerPhi[ # ]^2 ] ] & ]

Prog

(PARI) { n=0; for (m=1, 10^10, if (issquare(m^2 + eulerphi(m)^2), write("b066763.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 23 2010

Crossrefs

Sequence in context: A084821 A345654 A298462 * A164788 A033849 A194715

Adjacent sequences: A066760 A066761 A066762 * A066764 A066765 A066766

Keyword

nonn

Author

Joseph L. Pe, Jan 17 2002

Status

approved