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, 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

Author

N. J. A. Sloane, Sep 02 2017

Keywords

• nonn
• look

Comments

The logarithmic scatterplot of this sequence shows a banded structure similar to that of A092694. - Rémy Sigrist, Sep 03 2017

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• 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]

Crossrefs

Cf. A000010, A092694, A291783.

Programs

Mathematica

Table[Times @@ FixedPointList[EulerPhi, n], {n, 44}] (* Michael De Vlieger, Sep 03 2017 *)

Formula

a(n) = n * A092694(n). - Rémy Sigrist, Sep 03 2017