A239520 Prime powers (A025475) such that the distance to the nearest prime power is a triangular number (A000217).
1, 4, 8, 9, 49, 64, 125, 128, 2187, 2197, 654481, 657721, 1442401, 1442897, 1708249, 7252249, 7946761, 13053769, 13082689, 21557449, 39677401, 39702601, 86136961, 86174089, 106729561, 106770889, 184063489, 253987969, 302516449, 626550961, 626651089, 844425481
Offset: 1