A321339 a(1)=1; thereafter a(n) = a(n-1) * prime(a(n-1))^(n-1).

1, 2, 18, 4085658, 94856826320432984953640661130233988218

Offset

1,2

Comments

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).

An infinite and monotonically increasing sequence. Grows fast enough that a(6) and later terms are too large to display in full.

Links

Table of n, a(n) for n=1..5.

Example

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.

Mathematica

Nest[Append[#, #[[-1]] Prime[#[[-1]] ]^Length@ #] &, {1}, 4] (* Michael De Vlieger, Nov 05 2018 *)
nxt[{n_, a_}]:={n+1, a*Prime[a]^n}; NestList[nxt, {1, 1}, 4][[All, 2]] (* Harvey P. Dale, May 28 2019 *)

Prog

(PARI) apply( a(n) = prod(i=1, n-1, prime(a(i))^i), [1..5] )

Crossrefs

Somewhat similar to A007097.

Cf. A321340.

Sequence in context: A007184 A067765 A293242 * A086367 A321340 A221229

Adjacent sequences: A321336 A321337 A321338 * A321340 A321341 A321342

Keyword

nonn

Author

Russell Y. Webb, Nov 05 2018

Status

approved