What is the logic in this number sequence?

With $$a_n=1+\frac{n(n+1)(n-1)}2,$$ the next term would be 61 instead.

Seriously, number sequences are highly arbitrary. Who would guess that the next number after $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59$ is $60$ - because it lists the orders of non-trivial simple groups?