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%I #19 Jun 24 2022 05:25:17
%S 6,12,18,24,30,36,42,48,54,60,66,72,84,90,96,108,120,126,132,144,150,
%T 162,168,180,192,198,210,216,234,240,252,264,270,276,288,294,300,306,
%U 324,330,336,360,378,384,396,420,432,450,462,468,480,486,504,528,540,546
%N Numbers m such that there is at least one pair (x,y) 1 <= x <= y <= m such that 1/x + 1/y + 1/m = 1/phi(m).
%C It seems that necessarily a(n) == 0 (mod 6).
%C This is not true. The terms that are not divisible by 6 are 3850, 7700, 13300, 14210, 15400, ... . - _Amiram Eldar_, Jun 24 2022
%H Amiram Eldar, <a href="/A078596/b078596.txt">Table of n, a(n) for n = 1..500</a>
%e From _Amiram Eldar_, Jun 24 2022: (Start)
%e m = 6 is a term since for x = y = 6 we have 1/x + 1/y + 1/m = 1/6 + 1/6 + 1/6 = 1/2 = 1/phi(6).
%e m = 3850 is a term since for x = 3300 and y = 3696 we have 1/x + 1/y + 1/m = 1/3300 + 1/3696 + 1/3850 = 1/1200 = 1/phi(3850). (End)
%t q[m_] := Module[{s = 1/EulerPhi[m] - 1/m, k}, AnyTrue[Range[m], 1/# < s && IntegerQ[k = 1/(s - 1/#)] && 0 < k <= m &]]; Select[Range[600], q] (* _Amiram Eldar_, Jun 24 2022 *)
%Y Cf. A000010.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Dec 08 2002
%E 3 missing terms inserted and more terms added by _Amiram Eldar_, Jun 24 2022
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