A333373 a(n) = n + 1 for n <= 1; thereafter a(n) = a(n-1) * prime(gpf(a(n-1))).

1, 2, 6, 30, 330, 10230, 1299210, 921139890, 4956653748090, 261270175715571990, 169405230502395438168090, 1649555141343581679123602303970, 287748466487735183193170029972221262770, 1052440045241486547790272887133572295775622539770

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2020

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A006450, A006530, A007097, A052126, A076146, A156061.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = a[n - 1] Prime[FactorInteger[a[n - 1]][[-1, 1]]]; Table[a[n], {n, 0, 13}]
Table[Times @@ NestList[Prime@# &, 1, n], {n, 0, 13}]

Formula

a(n) = Product_{k=0..n} A007097(k).

A156061(a(n+1)) = a(n).

A052126(a(n+1)) = a(n).