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

10, 14, 20, 28, 40, 56, 80, 112, 160, 224, 320, 448, 640, 896, 1280, 1792, 2560, 3584, 5120, 7168, 10240, 14336, 20480, 28672, 40960, 57344, 81920, 114688, 163840, 229376, 327680, 458752, 655360, 917504, 1310720, 1835008, 2621440, 3670016, 5242880, 7340032, 10485760

Offset: 0

Author

Jason Earls, Aug 31 2001

Keywords

• nonn
• easy

Comments

Previous name was: t(n) = z(n) where t(n)= |eulerphi(n)-n| and z(n)= t(t(n)-n).

Links

• Amiram Eldar, Table of n, a(n) for n = 0..6637
• Ralf Stephan, Prove or disprove: 100 conjectures from the OEIS, arXiv:math/0409509 [math.CO], 2004.
• Lawrence Sze, Conjecture 36 (at archive.org).
• Lawrence Sze, Conjecture 36 - from OEIS - a.k.a. A063920, preprint, 2004. [cached copy]
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A070875 (the same sequence, if we omit the two initial terms).

Programs

Magma

[(12-2*(-1)^n)*2^Floor(n/2): n in [0..50]]; // Vincenzo Librandi, Feb 29 2016

Mathematica

CoefficientList[Series[(10 + 14 x) / (1 - 2 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 29 2016 *)

PARI

t(n) = abs(eulerphi(n)-n); z(n) = t(t(n)-n);
for(n=1,113, if(t(n)==z(n),print1(n, ", ")))

Formula

G.f.: (10 + 14x)/(1 - 2x^2).

a(n) = (12-2*(-1)^n) * 2^floor(n/2). - Ralf Stephan, Jul 19 2013

Sum_{n>=0} 1/a(n) = 12/35. - Amiram Eldar, Mar 28 2022

Extensions

Better name from Ivan Neretin, Feb 28 2016