%I #9 Aug 17 2017 05:58:53

%S 0,0,6,84,1400,25590,516432

%N Number of functions on a finite set that are not obtainable by any composition power (excluding identity as power).

%C a(n) is the number of functions on a finite set {1,...,n} that are not composition powers of any other function or powers(>1) of itself.

%C Hard to compute for n>7, as the number of functions to test is n^n.

%F a(n) = n^n - A163948(n).

%e For n=2, the set is {1,2} and we have 4 functions: the constants 1 and 2, the identity, and the transposition. Any composition power of a constant function or of identity is the function itself. Odd composition powers of the transposition give the transposition. Thus all 4 functions are represented.

%e For n=3, the set is {1,2,3} and f:{1,2,3}->{1,1,2} cannot be represented by composition powers of any other function, or powers of itself (as fof gives the constant function=1). There are 6 functions in this situation (similar).

%Y Cf. A102687, A163859, A163860, A163861, A163948.

%K more,hard,nonn

%O 1,3

%A _Carlos Alves_, Aug 06 2009