After 10 + days calculating, I got the following sequence : {13, 31, 46, 63, 81, 97, 112, 130, 148, 162, 180, 193, 211, 229, 244, 262, 277, 297, 310, 331, 343, 360, 378, 396, 406, 423, 436, 454, 469, 484487, 513517}
The conclusion seems correct at least for 1 <= n <= 31.
a (n) appears to be approximately equal to 16.5*n.