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A291782 Let f_k(n) be the result of applying phi (the Euler totient function A000010) k times to n; a(n) = n*Product_{k=1..oo} f_k(n). 1

%I

%S 1,2,6,8,40,12,84,64,108,80,880,96,1248,168,960,1024,17408,216,4104,

%T 1280,2016,1760,40480,1536,32000,2496,5832,2688,77952,1920,59520,

%U 32768,42240,34816,53760,3456,127872,8208,59904,40960,1679360,4032,173376,56320

%N Let f_k(n) be the result of applying phi (the Euler totient function A000010) k times to n; a(n) = n*Product_{k=1..oo} f_k(n).

%C The logarithmic scatterplot of this sequence shows a banded structure similar to that of A092694. - _Rémy Sigrist_, Sep 03 2017

%H Rémy Sigrist, <a href="/A291782/b291782.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="http://math.dartmouth.edu/~carlp/iterate.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.

%H Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="/A000010/a000010_1.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]

%F a(n) = n * A092694(n). - _Rémy Sigrist_, Sep 03 2017

%e Under phi, 7 -> 6 -> 2 -> 1, so a(7) = 7*6*2 = 84.

%t Table[Times @@ FixedPointList[EulerPhi, n], {n, 44}] (* _Michael De Vlieger_, Sep 03 2017 *)

%Y Cf. A000010, A092694, A291783.

%K nonn,look

%O 1,2

%A _N. J. A. Sloane_, Sep 02 2017

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Last modified September 23 03:00 EDT 2020. Contains 337291 sequences. (Running on oeis4.)