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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(n-1) divides a(n) whenever a(n-1) 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(n-1). 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.
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