

A077090


When iteration of f(x) = phi(sigma(x)  phi(x)) is started at initial values listed here it ends up in a cycle of length greater than 1.


8



36, 40, 48, 50, 52, 60, 64, 66, 72, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 100, 102, 105, 106, 108, 110, 112, 114, 116, 117, 118, 120, 122, 123, 124, 126, 128, 130, 132, 135, 136, 138, 140, 141, 142, 144, 146, 147, 148, 150, 152, 154, 156, 159, 160, 162, 164
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OFFSET

1,1


COMMENTS

Below 2000 there are only these two cycles of length 3: 36, 78, 48; and 144, 280, 192.
For most composite numbers below 80, the iterated trajectory of f settles on a singlenumber cycle of 4; those numbers are not in this sequence.  Alonso del Arte, Nov 29 2013


LINKS



EXAMPLE

36 is in the sequence because f(36) = 78, f(78) = 48 and f(48) = 36, which is a cycle of length 3.
38 is not in the sequence because iterating f from 38 gives the trajectory 38, 12, 8, 10, 6, 4, 4, 4, ... where the cycle has a length of 1.


MATHEMATICA

f[x_] := EulerPhi[DivisorSigma[1, x]  EulerPhi[x]]; Do[s = NestList[f, n, 100]; s1 = Part[s, 98]; s2 = Part[s, 99]; s3 = Part[s, 100]; If[ !Equal[s1, s2], k = k + 1; Print[{k, n, s1, s2, s3}]], {n, 2, 1000}]
f[n_] := EulerPhi[DivisorSigma[1, n]EulerPhi[n]]; cycleQ[n_] := With[{nn = NestWhileList[f, n, Unequal, All]}, nn[[1]] != nn[[2]]]; Select[Range[200], cycleQ] (* JeanFrançois Alcover, Nov 29 2013 *)


PROG

(PARI) f(x)=if(x>35, eulerphi(sigma(x)eulerphi(x)), 1)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



