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A063920 Numbers k such that k = 2*phi(k) + phi(phi(k)).

%I A063920 #49 Mar 28 2022 07:42:27
%S A063920 10,14,20,28,40,56,80,112,160,224,320,448,640,896,1280,1792,2560,3584,
%T A063920 5120,7168,10240,14336,20480,28672,40960,57344,81920,114688,163840,
%U A063920 229376,327680,458752,655360,917504,1310720,1835008,2621440,3670016,5242880,7340032,10485760
%N A063920 Numbers k such that k = 2*phi(k) + phi(phi(k)).
%C A063920 Previous name was: t(n) = z(n) where t(n)= |eulerphi(n)-n| and z(n)= t(t(n)-n).
%H A063920 Amiram Eldar, <a href="/A063920/b063920.txt">Table of n, a(n) for n = 0..6637</a>
%H A063920 Ralf Stephan, <a href="https://arxiv.org/abs/math/0409509">Prove or disprove: 100 conjectures from the OEIS</a>, arXiv:math/0409509 [math.CO], 2004.
%H A063920 Lawrence Sze, <a href="http://web.archive.org/web/20051107224725/http://lsze.cosam.calpoly.edu/A063920.pdf">Conjecture 36</a> (at archive.org).
%H A063920 Lawrence Sze, <a href="/A063920/a063920.pdf">Conjecture 36 - from OEIS - a.k.a. A063920</a>, preprint, 2004. [cached copy]
%H A063920 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A063920 G.f.: (10 + 14x)/(1 - 2x^2).
%F A063920 a(n) = (12-2*(-1)^n) * 2^floor(n/2). - _Ralf Stephan_, Jul 19 2013
%F A063920 Sum_{n>=0} 1/a(n) = 12/35. - _Amiram Eldar_, Mar 28 2022
%t A063920 CoefficientList[Series[(10 + 14 x) / (1 - 2 x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 29 2016 *)
%o A063920 (PARI) t(n) = abs(eulerphi(n)-n); z(n) = t(t(n)-n);
%o A063920 for(n=1,113, if(t(n)==z(n),print1(n, ", ")))
%o A063920 (Magma) [(12-2*(-1)^n)*2^Floor(n/2): n in [0..50]]; // _Vincenzo Librandi_, Feb 29 2016
%Y A063920 Cf. A070875 (the same sequence, if we omit the two initial terms).
%K A063920 nonn,easy
%O A063920 0,1
%A A063920 _Jason Earls_, Aug 31 2001
%E A063920 Better name from _Ivan Neretin_, Feb 28 2016