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Numbers k that divide phi(k)^2 + sigma(k)^2.
1

%I #17 Aug 20 2021 22:49:11

%S 1,2,10,45,65,180,212,222,369,588,810,864,1274,1521,1836,2548,2940,

%T 3114,3552,4770,5496,5684,6027,6642,8820,9140,10464,10614,13311,14688,

%U 15210,20737,21600,22776,26900,27000,27270,28476,28518,42212,42336

%N Numbers k that divide phi(k)^2 + sigma(k)^2.

%C a(275) > 7*10^7. - _G. C. Greubel_, Oct 15 2018

%H G. C. Greubel, <a href="/A068484/b068484.txt">Table of n, a(n) for n = 1..274</a>

%p with(numtheory): select(n->modp(phi(n)^2+sigma(n)^2,n)=0,[$1..42500]); # _Muniru A Asiru_, Oct 16 2018

%t Select[Range[7000], IntegerQ[(EulerPhi[#]^2 + DivisorSigma[1, #]^2)/#] &] (* _G. C. Greubel_, Oct 15 2018 *)

%o (GAP) Filtered([1..42500],n->(Phi(n)^2+Sigma(n)^2) mod n=0); # _Muniru A Asiru_, Oct 16 2018

%Y Cf. A072861 (sigma(n)^2), A127473 (phi(n)^2).

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Mar 10 2002