Let prime(j)# denote the product of the first j primes, A002110(j); then
a(1) = prime(1)# = 2,
a(2) = 6*prime(4)# = 1260,
a(3) = 2880*prime(8)# = 2.7935...*10^10,
a(4) = 907200*prime(16)# = 2.9564...*10^25,
a(5) >= 259459200*prime(30)# = 8.2015...*10^54,
a(6) >= 3238237626624000*prime(52)# = 3.4403...*10^111,
a(7) >= 248818180782850398720000*prime(91)# = 5.4351...*10^218.
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