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A063920
Numbers k such that k = 2*phi(k) + phi(phi(k)).
2
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
0,1
COMMENTS
Previous name was: t(n) = z(n) where t(n)= |eulerphi(n)-n| and z(n)= t(t(n)-n).
LINKS
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]
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
MATHEMATICA
CoefficientList[Series[(10 + 14 x) / (1 - 2 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 29 2016 *)
PROG
(PARI) t(n) = abs(eulerphi(n)-n); z(n) = t(t(n)-n);
for(n=1, 113, if(t(n)==z(n), print1(n, ", ")))
(Magma) [(12-2*(-1)^n)*2^Floor(n/2): n in [0..50]]; // Vincenzo Librandi, Feb 29 2016
CROSSREFS
Cf. A070875 (the same sequence, if we omit the two initial terms).
Sequence in context: A031274 A272375 A246473 * A269703 A057487 A073486
KEYWORD
nonn,easy
AUTHOR
Jason Earls, Aug 31 2001
EXTENSIONS
Better name from Ivan Neretin, Feb 28 2016
STATUS
approved