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A097005
A062401(x) is iterated. Initial value = n!. a(n) is the path-length of trajectory = count of transients and recurrent terms, i.e., all distinct states arising in trajectory.
1
1, 1, 1, 2, 3, 3, 1, 9, 6, 14, 2, 51, 35, 81, 32, 31
OFFSET
0,4
FORMULA
a(n) = A096859(n!) = A096859(A000142(n)). - Michel Marcus, Jul 27 2017
EXAMPLE
n=10: 10! = 3628800; trajectory ={3628800, 5702400, 5702400, ...} a(10) = 2, one transient and 1 cycle term.
MATHEMATICA
fs[x_]:=EulerPhi[DivisorSigma[1, x]] itef[x_, len_]:=NestList[fs, x, len] Table[Length[Union[itef[w!, 1000]]], {w, 0, 16}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Labos Elemer, Jul 22 2004
STATUS
approved