Power statistics of a finite group

Definition
The power statistics of a finite group $$G$$ of order $$n$$ can be viewed in the following ways:


 * 1) The non-cumulative power statistics is a function from the set of divisors of $$n$$ to the nonnegative integers, which sends $$d$$ to the number of elements $$g \in G$$ for which there exists $$h \in G$$ satisfying $$h^d = g$$ but such that there is no larger divisor $$d'$$ of $$n$$ for which there exists $$k \in G$$ with $$k^{d'} = g$$.
 * 2) The cumulative power statistics is a function from the set of divisors of $$n$$ to the nonnegative integers, which sends $$d$$ to the number of elements $$g \in G$$ for which there exists $$h \in G$$ satisfying $$h^d = g$$.

Similar statistics

 * Order statistics of a finite group: This gives information on the number of elements of each order.
 * Order-cum-power statistics of a finite group: This gives information on the number of elements of a given order that arise as given powers.

Related equivalence relations

 * Power statistics-equivalent finite groups