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A116007 Numbers k such that k + sigma(k) + phi(k) is a fourth power. 3

%I #15 Dec 15 2023 06:19:31

%S 81,18904,176705,204576,534160,1362561,1366633,1698256,1866768,

%T 2034576,2523024,2909656,3380856,7217649,9439473,9454609,11197696,

%U 12866040,29508673,32363424,34142545,34682089,46426160,46448824,53445456,57807984,58298881,81378529,98156353

%N Numbers k such that k + sigma(k) + phi(k) is a fourth power.

%H Amiram Eldar, <a href="/A116007/b116007.txt">Table of n, a(n) for n = 1..108</a>

%e 81 + sigma(81) + phi(81) = 4^4.

%t Select[Range[2*10^6], IntegerQ[Surd[# + DivisorSigma[1, #] + EulerPhi[#], 4]] &] (* _Amiram Eldar_, Dec 15 2023 *)

%o (PARI) isok(n) = ispower(n + sigma(n) + eulerphi(n), 4); \\ _Michel Marcus_, Jan 25 2014

%Y Cf. A000010, A000203, A116008, A116009.

%K nonn

%O 1,1

%A _Giovanni Resta_, Feb 13 2006

%E a(15)-a(25) from _Donovan Johnson_, Jul 02 2010

%E a(26)-a(29) from _Amiram Eldar_, Dec 15 2023

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)