A228593 Products of 2 successive primorials.

2, 12, 180, 6300, 485100, 69369300, 15330615300, 4951788741900, 2163931680210300, 1443342430700270100, 1297564845199542819900, 1488306877443875614425300, 2257761533082359307083180100, 3980433582824199458387646516300, 8044456270887707105401433609442300

Offset: 1

Author

Arkadiusz Wesolowski, Aug 27 2013

Keywords

• easy
• nonn

Comments

No sum of any number of terms is a perfect power.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..196
• Wikipedia, Perfect power.

Crossrefs

Cf. A000040, A001597, A006094, A002110.

Programs

Magma

[n le 1 select 2 else Self(n-1)*NthPrime(n-1)*NthPrime(n): n in [1..14]];

Mathematica

nxt[{n_,a_}]:={n+1,a Prime[n]Prime[n+1]}; NestList[nxt,{1,2},20][[All,2]] (* Harvey P. Dale, Feb 19 2020 *)

PARI

a(n) = vecprod(primes(n-1))*vecprod(primes(n)); \\ Michel Marcus, Aug 11 2023

Formula

a(1) = 2; a(n) = 2*(Product_{i=1..n-1} A006094(i)), n >= 2.

a(n) = A002110(n-1)*A002110(n); n >= 1. - David James Sycamore, Jul 13 2023

a(1) = 2, for n>1 a(n) = a(n-1)*prime(n-1)*prime(n). - David James Sycamore, Jul 15 2023