The terms and their factorizations begin:
a(0) = 2 = 2
a(1) = 6 = 2 * 3
a(2) = 30 = 2 * 3* 5
a(3) = 2002 = 2 * 7*11*13
a(4) = 92378 = 2 * 11*13*17*19
a(5) = 13357342 = 2 * 17*19*23*29*31
a(6) = 2697562774 = 2 * 23*29*31*37*41*43
a(7) = 292157776958 = 2 * 29*31*37*41*43*47*53
a(8) = 36257787561098 = 2 * 31*37*41*43*47*53*59*61
a(9) = 5563815981553006 = 2 * 37*41*43*47*53*59*61*67*71
a(10) = 406158566653369438 = 2 * 37*41*43*47*53*59*61*67*71*73
...
a(n1) divides a(n) whenever a(n1) and a(n) have the same smallest odd prime factor; this happens at n = 2, 10, 12, 14, 19, 20, ..., which are the indices at which the largest prime factor of a(n) is less than twice the smallest prime factor of a(n1). E.g., both a(9) and a(10) have 37 as their smallest odd prime factor, and 73 (the largest prime factor of a(10)) < 74 = 2*37.
