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Numbers n such that phi(n) * sigma(n) + 9 is a perfect square.
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%I #16 Sep 08 2022 08:44:40

%S 10,12,27,38,90,95,110,114,142,152,230,344,356,395,442,474,639,684,

%T 738,973,1098,1349,1558,1562,1566,1956,2365,2392,2408,2438,2451,2484,

%U 2492,2666,2838,3145,3236,3377,3730,3774,3886,4448,4833,5356

%N Numbers n such that phi(n) * sigma(n) + 9 is a perfect square.

%H Vincenzo Librandi, <a href="/A015728/b015728.txt">Table of n, a(n) for n = 1..210</a>

%H Richard K. Guy, <a href="http://www.jstor.org/stable/2974586">Divisors and desires</a>, Amer. Math. Monthly, 104 (1997), 359-360.

%t Select[Range[10000], IntegerQ[Sqrt[EulerPhi[#]DivisorSigma[1, #] + 9]] &] (* _Vincenzo Librandi_, Mar 14 2014 *)

%o (Magma) [n: n in [1..6000] | IsSquare(EulerPhi(n) * SumOfDivisors(n) + 9)]; // _Vincenzo Librandi_, Mar 14 2014

%K nonn

%O 1,1

%A _Robert G. Wilson v_