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%I #19 Aug 29 2024 09:15:08
%S 1,1,1,2,3,3,1,9,6,14,2,51,35,81,32,31
%N 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.
%F a(n) = A096859(n!) = A096859(A000142(n)). - _Michel Marcus_, Jul 27 2017
%e n=10: 10! = 3628800; trajectory ={3628800, 5702400, 5702400, ...} a(10) = 2, one transient and 1 cycle term.
%t fs[x_]:=EulerPhi[DivisorSigma[1,x]] itef[x_,len_]:=NestList[fs,x,len] Table[Length[Union[itef[w!,1000]]],{w,0,16}]
%Y Cf. A000010, A000142, A000203, A062401, A096859.
%K nonn,more
%O 0,4
%A _Labos Elemer_, Jul 22 2004