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A092694 Product of iterated phi(n). 3

%I

%S 1,1,2,2,8,2,12,8,12,8,80,8,96,12,64,64,1024,12,216,64,96,80,1760,64,

%T 1280,96,216,96,2688,64,1920,1024,1280,1024,1536,96,3456,216,1536,

%U 1024,40960,96,4032,1280,1536,1760,80960,1024,4032,1280,32768,1536,79872,216

%N Product of iterated phi(n).

%C A logarithmic plot of this sequence shows an unusual banded structure.

%H T. D. Noe, <a href="/A092694/b092694.txt">Table of n, a(n) for n=1..10000</a>

%H T. D. Noe, <a href="/A092694/a092694.gif">Plot of A092694</a>

%F a(1) = 1, a(n) = phi(n) * a(phi(n))

%e a(100) = 40960 because the iterations of phi (40, 16, 8, 4, 2, 1) have a product of 40960.

%t nMax=100; a=Table[1, {nMax}]; Do[e=EulerPhi[n]; a[[n]]=e*a[[e]], {n, 2, nMax}]; a

%o (Haskell)

%o a092694 n = snd $ until ((== 1) . fst) f (a000010 n, 1) where

%o f (x, p) = (a000010 x, p * x)

%o -- _Reinhard Zumkeller_, Jan 30 2014

%Y Cf. A003434 (iterations of phi(n) needed to reach 1), A092693 (iterated phi sum).

%Y Cf. A000010.

%K nonn,look

%O 1,3

%A _T. D. Noe_, Mar 04 2004

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)