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, 2, 3, 3, 1, 9, 6, 14, 2, 51, 35, 81, 32, 31

Offset: 0

Author

Labos Elemer, Jul 22 2004

Keywords

• nonn
• more

Examples

			n=10: 10! = 3628800; trajectory ={3628800, 5702400, 5702400, ...} a(10) = 2, one transient and 1 cycle term.
		

Crossrefs

Cf. A000010, A000142, A000203, A062401, A096859.

Programs

Mathematica

fs[x_]:=EulerPhi[DivisorSigma[1,x]] itef[x_,len_]:=NestList[fs,x,len] Table[Length[Union[itef[w!,1000]]],{w,0,16}]

Formula

a(n) = A096859(n!) = A096859(A000142(n)). - Michel Marcus, Jul 27 2017