

A096995


Number of transient terms if f(x) = sigma(phi(x)) = A062402 is iterated at initial value = 2^n.


4



0, 1, 1, 1, 1, 1, 3, 3, 1, 2, 3, 5, 2, 3, 6, 15, 1, 6, 8, 3, 15, 9, 4, 65, 44, 82, 83, 77, 75, 48, 26, 43, 1
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OFFSET

0,7


COMMENTS

For initial value = 2^33 more than 38000 iterations did not lead to a recurrent term, so possibly there is no cycle. a(34) through a(39) are 8, 52, 71, 24, 40, 12.  Klaus Brockhaus, Jul 19 2007


LINKS



EXAMPLE

Trajectory of 2^0 is 1,1, ...; there are zero transient terms preceding the 1cycle (1), so a(0) = 0.
Trajectory of 2^14 is 16384, 16383, 34200, 30480, 26520, 16380, 10200, 6138, 6045, 9906, 9920, 12264, 10200, ...; there are six transient terms preceding the 6cycle (10200, 6138, 6045, 9906, 9920, 12264), so a(14) = 6.


MATHEMATICA

With[{nn = 10^4}, Table[Count[Values@ PositionIndex@ NestList[DivisorSigma[1, EulerPhi@ #] &, 2^n, nn], _?(Length@ # == 1 &)], {n, 0, 60}] /. m_ /; m == nn + 1 > 1] (* Michael De Vlieger, Jul 24 2017 *)


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



