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Numbers k such that sigma(k)*phi(k)*k is a square.
1

%I #14 Jul 22 2021 02:00:34

%S 1,6,40,84,162,672,2268,2480,3159,18144,58752,80262,91000,126360,

%T 140800,170688,358668,634725,718848,1063300,1089270,1255338,1701000,

%U 2319525,2869344,4189500,4608576,5642000,7834320,8506400,9450000,10480640,15049125,17716608,18674500

%N Numbers k such that sigma(k)*phi(k)*k is a square.

%H Amiram Eldar, <a href="/A114079/b114079.txt">Table of n, a(n) for n = 1..100</a>

%e sigma(84)*phi(84)*84 = 451584 = 672^2.

%t Select[Range[10^5], IntegerQ @ Sqrt[# * EulerPhi[#] * DivisorSigma[1, #]] &] (* _Amiram Eldar_, Aug 13 2019 *)

%o (PARI) isok(n) = issquare(sigma(n)*eulerphi(n)*n); \\ _Michel Marcus_, Aug 13 2019

%Y Cf. A000010, A000203.

%K nonn

%O 1,2

%A _Giovanni Resta_, Feb 13 2006

%E More terms from _Amiram Eldar_, Aug 13 2019