%I #18 May 28 2019 15:33:00
%S 1,2,18,4085658,94856826320432984953640661130233988218
%N a(1)=1; thereafter a(n) = a(n-1) * prime(a(n-1))^(n-1).
%C The prime factorization of a(n) describes all previous terms in the sequence: a(n) = prime(a(1))^1 * prime(a(2))^2 * prime(a(3))^3 * ...* prime(a(n-1))^(n-1).
%C An infinite and monotonically increasing sequence. Grows fast enough that a(6) and later terms are too large to display in full.
%e 4085658 = 2 * 3^2 *61^3 = prime(1)^1 * prime(2)^2 * prime(18)^3. The previous values in the sequence can be read from this factorization: the 3rd is 18, the 2nd is 2, the 1st is 1.
%t Nest[Append[#, #[[-1]] Prime[#[[-1]] ]^Length@ #] &, {1}, 4] (* _Michael De Vlieger_, Nov 05 2018 *)
%t nxt[{n_,a_}]:={n+1,a*Prime[a]^n}; NestList[nxt,{1,1},4][[All,2]] (* _Harvey P. Dale_, May 28 2019 *)
%o (PARI) apply( a(n) = prod(i=1, n-1, prime(a(i))^i), [1..5] )
%Y Somewhat similar to A007097.
%Y Cf. A321340.
%K nonn
%O 1,2
%A _Russell Y. Webb_, Nov 05 2018