This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
Let pn be the n th prime number. In this note, we study strictly increasing sequences of positive integers An such that the limit limn→∞ (A1A2· · · An)1/pn = e holds. This limit formula is in fact a generalization of some previously known results. Furthermore, some other generalizations are established.