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A066785
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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.
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1
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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603^2 + phi(603)^2 + sigma(603)^2 = 603^2 + 396^2 + 884^2 = 1141^2, so 603 is a term of the sequence.
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MATHEMATICA
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Select[ Range[ 1, 10^6 ], IntegerQ[ Sqrt[ #^2 + DivisorSigma[ 1, # ]^2 + EulerPhi[ # ]^2 ] ] & ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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