A163947 Number of functions on a finite set that are not obtainable by any composition power (excluding identity as power).

0, 0, 6, 84, 1400, 25590, 516432

Offset: 1

Author

Carlos Alves, Aug 06 2009

Keywords

• more
• hard
• nonn

Comments

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.

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

Examples

			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.
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).
		

Crossrefs

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

Formula

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