cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

This page as a plain text file.
%I A291782 #17 Sep 03 2017 21:33:46
%S A291782 1,2,6,8,40,12,84,64,108,80,880,96,1248,168,960,1024,17408,216,4104,
%T A291782 1280,2016,1760,40480,1536,32000,2496,5832,2688,77952,1920,59520,
%U A291782 32768,42240,34816,53760,3456,127872,8208,59904,40960,1679360,4032,173376,56320
%N 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).
%C A291782 The logarithmic scatterplot of this sequence shows a banded structure similar to that of A092694. - _Rémy Sigrist_, Sep 03 2017
%H A291782 Rémy Sigrist, <a href="/A291782/b291782.txt">Table of n, a(n) for n = 1..10000</a>
%H A291782 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 A291782 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 A291782 a(n) = n * A092694(n). - _Rémy Sigrist_, Sep 03 2017
%e A291782 Under phi, 7 -> 6 -> 2 -> 1, so a(7) = 7*6*2 = 84.
%t A291782 Table[Times @@ FixedPointList[EulerPhi, n], {n, 44}] (* _Michael De Vlieger_, Sep 03 2017 *)
%Y A291782 Cf. A000010, A092694, A291783.
%K A291782 nonn,look
%O A291782 1,2
%A A291782 _N. J. A. Sloane_, Sep 02 2017