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A376848 Numbers k such that phi(k + phi(k)) = phi(k) + phi(phi(k)), where phi = A000010.

%I A376848 #13 Oct 08 2024 07:19:20
%S A376848 2,5,9,10,14,18,20,27,28,36,38,40,46,54,56,72,76,78,80,81,92,108,112,
%T A376848 144,152,156,160,162,184,216,224,234,243,258,288,294,304,312,320,324,
%U A376848 368,432,438,448,468,486,516,526,570,576,588,608,609,624,640,648,702,718,729,736,754,774,864,876
%N A376848 Numbers k such that phi(k + phi(k)) = phi(k) + phi(phi(k)), where phi = A000010.
%C A376848 If k is in A126955, then 8*k + 6 is a term.
%H A376848 Robert Israel, <a href="/A376848/b376848.txt">Table of n, a(n) for n = 1..10000</a>
%e A376848 a(4) = 10 is a term because phi(10) = 4, phi(4) = 2, and phi(10 + 4) = phi(14) = 6 = 4 + 2.
%p A376848 filter:= proc(k) uses numtheory; local s;
%p A376848  s:= phi(k);
%p A376848  phi(k+s) = s + phi(s)
%p A376848 end proc:
%p A376848 select(filter, [$1..1000]);
%t A376848 Select[Range[880], EulerPhi[ #+EulerPhi[#]]==EulerPhi[#]+EulerPhi[EulerPhi[#]] &] (* _Stefano Spezia_, Oct 07 2024 *)
%Y A376848 Cf. A000010, A126955, A376830, A376831, A376843, A376844, A376849, A376851.
%K A376848 nonn
%O A376848 1,1
%A A376848 _Robert Israel_, Oct 06 2024