  Let R be a Cohen-Macaulay local ring with a canonical module. We consider
Auslander's (higher) delta invariants of powers of certain ideals of R.
Firstly, we shall provide some conditions for an ideal to be a parameter ideal
in terms of delta invarints. As an application of this result, we give upper
bounds for orders of Ulrich ideals of R when R has Gorenstein punctured
spectrum. Secondly, we extend the definition of indices to the ideal case, and
generalize the result of Avramov-Buchweitz-Iyengar-Miller on the relationship
between the index and regularity.
