This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383044 #15 May 11 2025 18:39:00
%S A383044 4,6,8,10,12,14,16,20,24,28,32,40,48,56,64,70,80,94,96,112,128,140,
%T A383044 160,188,192,224,256,280,320,376,384,448,512,560,640,752,768,896,1024,
%U A383044 1120,1280,1504,1536,1792,2048,2240,2560,3008,3072,3584,4096,4480,5120,6016,6144,7168,8192,8960
%N A383044 Numbers m such that phi(m) + phi(m+phi(m)) = m where phi is the Euler totient function.
%C A383044 Empirical observation: Let phi(m) + phi(m + phi(m)) = A*m / B, GCD(A,B) = 1. For some (A,B) like (1,1) - this sequence, (2,3), (4,5), (4,7), (5,7), (7,9), (14,9), (8,11), ..., there exists (finitely/infinitely many ?) solutions to phi(m) + phi(m + phi(m)) = A*m / B. Experimentally it looks like for m = 3*A033845(n) = 18*A003586(n), phi(m) + phi(m + phi(m)) = 7*m / 9. - _Ctibor O. Zizka_, Apr 25 2025
%H A383044 Stefan Steinerberger, <a href="https://arxiv.org/abs/2504.08023">On an iterated arithmetic function problem of Erdos and Graham</a>, arXiv:2504.08023 [math.NT], 2025.
%t A383044 q[m_] := Module[{phi = EulerPhi[m]}, phi + EulerPhi[m + phi] == m]; Select[Range[10000], q] (* _Amiram Eldar_, Apr 14 2025 *)
%o A383044 (PARI) isok(m) = eulerphi(m) + eulerphi(m+eulerphi(m)) == m;
%Y A383044 Cf. A000010, A121048.
%K A383044 nonn
%O A383044 1,1
%A A383044 _Michel Marcus_, Apr 14 2025