Is it sufficient to rely on the call to prayer (adhan) from a computer program set to sound the adhan at its times, or is this not considered a sufficient adhan since it originates from a device?

If the recorded adhan is for reminding of prayer times, then there is no harm in it. However, if it is intended to be a legitimate adhan, replacing the muezzin, then it is not valid, and it is not the required legitimate adhan. Rather, it is an echo of an adhan. The adhan is an act of worship that cannot come from an inanimate object. It carries a great reward, as stated in the hadith: "If the people knew what was in the call (to prayer) and the first row, and they found no way to obtain it except by drawing lots, they would draw lots for it."