A253591 a(n) is the largest prime occurring (as a factor) in all terms up to A098550(n).
2, 3, 3, 3, 3, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31
Offset: 2