A066785 Numbers k such that (k, phi(k), sigma(k)) lies on a sphere with integral radius centered at the origin, i.e., k^2 + phi(k)^2 + sigma(k)^2 is a square.

603, 1414, 1444, 2093, 7434, 12822, 66584, 66960, 91000, 138645, 160130, 167400, 169212, 210476, 218592, 229026, 236572, 265977, 304128, 344790, 493722, 618570, 754110, 950158, 1091385, 1113480, 1760616, 1761409, 2116116, 2733131, 2776928

Offset: 1

Author

Joseph L. Pe, Jan 18 2002

Keywords

• nonn

Examples

			603^2 + phi(603)^2 + sigma(603)^2 = 603^2 + 396^2 + 884^2 = 1141^2, so 603 is a term of the sequence.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..82

Crossrefs

Cf. A066763, A066764.

Programs

Mathematica

Select[ Range[ 1, 10^6 ], IntegerQ[ Sqrt[ #^2 + DivisorSigma[ 1, # ]^2 + EulerPhi[ # ]^2 ] ] & ]

PARI

isok(k) = { issquare(k^2 + eulerphi(k)^2 + sigma(k)^2) } \\ Harry J. Smith, Mar 25 2010

Extensions

Terms a(25)-a(31) from Harry J. Smith, Mar 25 2010