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%I #9 Feb 20 2023 12:26:24
%S 0,0,2,1,0,0,0,1,2,2,0,1,0,4,4,1,0,2,0,5,4,4,0,3,4,4,4,7,0,0,0,1,6,2,
%T 2,3,0,6,2,7,0,2,0,9,6,4,0,3,0,4,6,9,0,4,2,9,4,2,0,1,0,4,4,1,4,4,0,9,
%U 4,4,0,5,0,4,8,9,2,6,0,7,0,2,0,3,4,4,8,9,0,2,0,11,8,4,0,3,0,2,6,9,0,6,0
%N Number of solutions 0<k<n to the equation phi(n) = phi(k) + phi(n-k), where phi is Euler's totient function.
%H Antti Karttunen, <a href="/A110174/b110174.txt">Table of n, a(n) for n = 1..65537</a>
%t a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; Table[Length[a[n]], {n, 150}]
%o (PARI) A110174(n) = { my(ph=eulerphi(n)); sum(k=1,n-1,(ph == (eulerphi(k)+eulerphi(n-k)))); }; \\ _Antti Karttunen_, Feb 20 2023
%Y Cf. A110173 (least k such that phi(n) = phi(k) + phi(n-k)).
%Y Cf. also A110177.
%K nonn,look
%O 1,3
%A _T. D. Noe_, Jul 15 2005
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