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%I #10 Nov 19 2020 18:11:33
%S 1,3,2,1,15,14,3,8,9,30,30,14,7,6,5,9,3,8,55,60,9,4,83,28,25,71,9,1,
%T 24,4,43,32,1523,30,13,9,35,3,21,24,17,18,7,8,99,166,5,4,3,32,205,6,
%U 36,18,19,19,40,78,9,8
%N Least positive integer m such that m + n divides phi(m)^2 + phi(n)^2, where phi(.) is Euler's totient function.
%C Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 except for n = 33.
%H Zhi-Wei Sun, <a href="/A248035/b248035.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1409.5685">A new theorem on the prime-counting function</a>, arXiv:1409.5685, 2014.
%e a(5) = 15 since 15 + 5 = 20 divides phi(15)^2 + phi(5)^2 = 8^2 + 4^2 = 80.
%e a(33) = 1523 since 1523 + 33 = 1556 divides phi(1523)^2 + phi(33)^2 = 1522^2 + 20^2 = 2316884 = 1489*1556.
%t Do[m=1;Label[aa];If[Mod[EulerPhi[m]^2+EulerPhi[n]^2,m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
%t lpim[n_]:=Module[{m=1,p2=EulerPhi[n]^2},While[Mod[p2+EulerPhi[m]^2,m+n]!=0,m++];m]; Array[lpim,60] (* _Harvey P. Dale_, Nov 19 2020 *)
%Y Cf. A000010, A247975, A248007, A248036.
%K nonn
%O 1,2
%A _Zhi-Wei Sun_, Sep 29 2014
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