%I #13 Oct 08 2024 07:19:20

%S 2,5,9,10,14,18,20,27,28,36,38,40,46,54,56,72,76,78,80,81,92,108,112,

%T 144,152,156,160,162,184,216,224,234,243,258,288,294,304,312,320,324,

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

%C If k is in A126955, then 8*k + 6 is a term.

%H Robert Israel, <a href="/A376848/b376848.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 10 is a term because phi(10) = 4, phi(4) = 2, and phi(10 + 4) = phi(14) = 6 = 4 + 2.

%p filter:= proc(k) uses numtheory; local s;

%p s:= phi(k);

%p phi(k+s) = s + phi(s)

%p end proc:

%p select(filter, [$1..1000]);

%t Select[Range[880], EulerPhi[ #+EulerPhi[#]]==EulerPhi[#]+EulerPhi[EulerPhi[#]] &] (* _Stefano Spezia_, Oct 07 2024 *)

%Y Cf. A000010, A126955, A376830, A376831, A376843, A376844, A376849, A376851.

%K nonn

%O 1,1

%A _Robert Israel_, Oct 06 2024