

A096857


a[n] is the length of terminal cycle of the trajectory of g[x]=sigma(phi(x)] if started at 2^n. Formally identical to A096852, but arguments are shifted by 1 and the iterated functions are different!.


7



1, 1, 2, 1, 3, 2, 2, 1, 2, 2, 6, 2, 1, 6, 2, 1, 2, 3, 11, 11, 2, 2, 15, 15, 18, 18, 18, 18, 12, 12, 12, 1
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OFFSET

1,3


COMMENTS

Offset=1 in contrast to A096852, where offset=0. Also the iterated functions deviate: A062401 iterated in A096852 and A062402 is repeated here; A096852(n)=A096857(n+1) appears to be true. While cyclelengths seem identical, the composition of cycles are mostly different!


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

n=5:iv=32 list={32,[31,72,60]} length=a(5)=3, while the parallel case of A096852(n)=b(n) is b[4] with [16,24,30] cycle.
Also A096857[11] starts with 2048 ends in 6cycle: {2048,2047,4123,10890,8928,[9906,9920,12264,10200,6138,6045],9906,..
while A096852[111]=6 and the relevant 6cycle is {1024,1936,3240,2640,[2880,3024,3840,3456,2560,1800],2880,... These are different cycles with identical lengths.
The initial value 146 leads to list with enormous terms.


MATHEMATICA

f[n_] := DivisorSigma[1, EulerPhi[n]]; g[n_] := Block[{l = NestWhileList[f, 2^n, UnsameQ, All]}, Subtract @@ Flatten[Position[l, l[[ 1]]]]]; Table[ g[n], {n, 25}] (* Robert G. Wilson v, Jul 21 2004 *)


CROSSREFS

Cf. A062401, A062402, A096852, A096858.
Sequence in context: A282463 A265337 A096852 * A303639 A090000 A109082
Adjacent sequences: A096854 A096855 A096856 * A096858 A096859 A096860


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 19 2004


STATUS

approved



