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%I #12 Apr 08 2020 18:43:03
%S 1,2,6,30,330,10230,1299210,921139890,4956653748090,
%T 261270175715571990,169405230502395438168090,
%U 1649555141343581679123602303970,287748466487735183193170029972221262770,1052440045241486547790272887133572295775622539770
%N a(n) = n + 1 for n <= 1; thereafter a(n) = a(n-1) * prime(gpf(a(n-1))).
%C For n > 1, a(n) belongs to A083207 (see "product" formula below and my Jan 16 2020 comment in A083207). - _Ivan N. Ianakiev_, Mar 17 2020
%F a(n) = Product_{k=0..n} A007097(k).
%F A156061(a(n+1)) = a(n).
%F A052126(a(n+1)) = a(n).
%e a(7) = a(6) * prime(gpf(a(6))) = prime(1) * prime(2) * prime(3) * prime(5) * prime(11) * prime(31) * prime(127) = 2 * 3 * 5 * 11 * 31 * 127 * 709 = 921139890.
%t a[0] = 1; a[n_] := a[n] = a[n - 1] Prime[FactorInteger[a[n - 1]][[-1, 1]]]; Table[a[n], {n, 0, 13}]
%t Table[Times @@ NestList[Prime@# &, 1, n], {n, 0, 13}]
%Y Cf. A006450, A006530, A007097, A052126, A076146, A156061.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 17 2020
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