A customary solution to reduce the energy consumption of wireless communication devices is to periodically put the radio into low-power sleep mode. A relevant problem is to schedule the wake-up of nodes in such a way as to ensure proper coordination among devices, respecting delay constraints while still saving energy. In this paper, we introduce a simple algebraic characterization of the problem of periodic wake-up scheduling under both energy consumption and delay constraints. We demonstrate that the general problem of wake-up times coordination is equivalent to integer factorization and discuss the implications on the design of efficient scheduling algorithms. We then propose simple polynomial time heuristic algorithms that can be implemented in a distributed fashion and present a message complexity of the order of the number of links in the network. Numerical results are provided in order to assess the performance of the proposed techniques when applied to wireless sensor networks.