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A066785 Numbers n such that (n, phi(n), sigma(n)) lies on a sphere with integral radius centered at the origin, i.e., n^2 + phi(n)^2 + sigma(n)^2 is a square. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

(PARI) { n=0; for (m=1, 10^10, if (issquare(m^2 + eulerphi(m)^2 + sigma(m)^2), write("b066785.txt", n++, " ", m); if (n==100, return)) ) } \\ Harry J. Smith, Mar 25 2010

CROSSREFS

Sequence in context: A145331 A252957 A348077 * A178032 A107256 A177685

Adjacent sequences:  A066782 A066783 A066784 * A066786 A066787 A066788

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Jan 18 2002

EXTENSIONS

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

STATUS

approved

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Last modified October 18 08:58 EDT 2021. Contains 348067 sequences. (Running on oeis4.)