A167747 a(n) = phi(6^n).
1, 2, 12, 72, 432, 2592, 15552, 93312, 559872, 3359232, 20155392, 120932352, 725594112, 4353564672, 26121388032, 156728328192, 940369969152, 5642219814912, 33853318889472, 203119913336832, 1218719480020992, 7312316880125952, 43873901280755712, 263243407684534272
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- D. Bevan, D. Levin, P. Nugent, J. Pantone, L. Pudwell, M. Riehl and M. L. Tlachac, Pattern avoidance in forests of binary shrubs, arXiv preprint arXiv:1510:08036 [math.CO], 2015-2016.
- Index entries for linear recurrences with constant coefficients, signature (6).
Programs
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Mathematica
Table[EulerPhi[6^n],{n,0,40}] -
PARI
a(n) = eulerphi(6^n); \\ Michel Marcus, Jan 02 2021
Formula
a(n+1) = 2*6^n. - Charles R Greathouse IV, Nov 12 2009
G.f.: (1-4x)/(1-6x). - Philippe Deléham, Oct 10 2011
a(n) = ((8*n-4)*a(n-1)-12*(n-2)*a(n-2))/n, a(0)=1, a(1)=2. - Sergei N. Gladkovskii, Jul 19 2012
Sum_{n>=0} 1/a(n) = 8/5. - Amiram Eldar, Jan 02 2021
From Amiram Eldar, May 08 2023: (Start)
Sum_{n>=0} (-1)^n/a(n) = 4/7.
Product_{n>=1} (1 - 1/a(n)) = A132022. (End)