

A096850


Consider iteration of the function f(x) = phi(sigma(x)) = A062401(x). Sequence gives numbers n such that the trajectory of n returns to n.


6



1, 2, 4, 6, 8, 12, 16, 24, 30, 48, 60, 72, 96, 128, 240, 432, 480, 576, 720, 864, 1200, 1280, 1512, 1536, 1728, 1800, 1860, 2016, 2560, 2880, 3024, 3456, 3840, 6912, 10368, 14080, 15552, 15840, 18144, 27648, 30976, 32768, 34560, 41472, 42240, 48384
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OFFSET

1,2


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..110


EXAMPLE

Examples of cycles: {[1], [2], [4, 6], [8], [12], [16, 30, 24], [48, 60], [72, 96], [128]}.
95 => 32 => 36 => 72 => 96 => 72 => ..., therefore 72 and 96 are in the sequence.


MATHEMATICA

a = {}; f[n_] := EulerPhi[ DivisorSigma[ 1, n]]; Do[ AppendTo[a, NestWhileList[f, n, UnsameQ, All][[ 1]]]; a = Union[a], {n, 10^6}]; Take[ a, 46] (* Robert G. Wilson v, Jul 21 2004 *)


PROG

(PARI) f(n)=eulerphi(sigma(n))
is(n)=my(t=f(n), h=f(t)); while(t!=h, t=f(t); h=f(f(h)); if(t==n, return(1))); t==n \\ Charles R Greathouse IV, Nov 27 2013


CROSSREFS

Cf. A062401, A095952A095956, A096887A096890, A096849A096851.
Sequence in context: A279537 A325238 A070175 * A250270 A062847 A001013
Adjacent sequences: A096847 A096848 A096849 * A096851 A096852 A096853


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 16 2004


EXTENSIONS

Edited and extended by Robert G. Wilson v, Jul 21 2004


STATUS

approved



