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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
1, 2, 6, 8, 40, 12, 84, 64, 108, 80, 880, 96, 1248, 168, 960, 1024, 17408, 216, 4104, 1280, 2016, 1760, 40480, 1536, 32000, 2496, 5832, 2688, 77952, 1920, 59520, 32768, 42240, 34816, 53760, 3456, 127872, 8208, 59904, 40960, 1679360, 4032, 173376, 56320
OFFSET
1,2
COMMENTS
The logarithmic scatterplot of this sequence shows a banded structure similar to that of A092694. - Rémy Sigrist, Sep 03 2017
LINKS
Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
FORMULA
a(n) = n * A092694(n). - Rémy Sigrist, Sep 03 2017
EXAMPLE
Under phi, 7 -> 6 -> 2 -> 1, so a(7) = 7*6*2 = 84.
MATHEMATICA
Table[Times @@ FixedPointList[EulerPhi, n], {n, 44}] (* Michael De Vlieger, Sep 03 2017 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
N. J. A. Sloane, Sep 02 2017
STATUS
approved