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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

%I

%S 603,1414,1444,2093,7434,12822,66584,66960,91000,138645,160130,167400,

%T 169212,210476,218592,229026,236572,265977,304128,344790,493722,

%U 618570,754110,950158,1091385,1113480,1760616,1761409,2116116,2733131,2776928

%N 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.

%H Harry J. Smith, <a href="/A066785/b066785.txt">Table of n, a(n) for n = 1..82</a>

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

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

%o (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

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jan 18 2002

%E Terms a(25) - a(31) from _Harry J. Smith_, Mar 25 2010

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Last modified December 4 18:08 EST 2021. Contains 349526 sequences. (Running on oeis4.)