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%I #3 Mar 30 2012 17:22:40
%S 6,30,49,81,91,95,115,121,155,187,205,210,221,243,254,259,287,298,299,
%T 329,341,355,361,377,403,415,437,451,469,473,502,533,551,559,565,611,
%U 625,629,649,655,662,667,674,679,685,703,713,731,737,746,767,779,781
%N Composite numbers n such that the equation phi(n)=phi(k)+phi(n-k) has no solution, where phi is Euler's totient function.
%C The only prime for which this equation has a solution is 3.
%t a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; t=Table[Length[a[n]], {n, 1000}]; Complement[Flatten[Position[t, 0]], Prime[Range[PrimePi[1000]]]]
%Y Cf. A110173 (least k such that phi(n)=phi(k)+phi(n-k)).
%K nonn
%O 1,1
%A _T. D. Noe_, Jul 15 2005