A165336 Numbers that eventually reach a cycle under "x -> sum of cubes of digits of x" (see A055012).

4, 13, 16, 22, 25, 28, 31, 40, 46, 49, 52, 55, 61, 64, 79, 82, 94, 97, 103, 106, 115, 127, 130, 133, 136, 151, 160, 163, 172, 199, 202, 205, 208, 217, 220, 229, 235, 238, 244, 250, 253, 256, 265, 271, 280, 283, 289, 292, 298, 301, 310, 313, 316, 325, 328, 331