A330769 a(n) = Product_{k=max(1,n)..2*n} prime(k).

1, 6, 105, 5005, 323323, 30808063, 3212440751, 435656388001, 63836474265323, 12091972151626183, 2500935283708076197, 497341164867050876831, 118511586608803381520987, 31379946324498560236786747, 8435082644934112984625042407, 2416160765991941154223875519233, 855269503485274999634523766244243

Offset

0,2

Comments

a(n) has lpf(a(n)) = omega(a(n)) = bigomega(a(n)), where lpf = A020639, omega = A001221, and bigomega = A001222. - Michael De Vlieger, Feb 07 2026

Links

Michael De Vlieger, Table of n, a(n) for n = 0..287

Alexander Dirmeier, On Metrics Inducing the Fürstenberg Topology on the Integers, arXiv:1912.11663 [math.GN], 2019. See p. 12.

Formula

a(n) = A002110(2*n)/A002110(n-1) for n>1.

For n > 0, a(n) = product of prime(i) for i in row n of A051162. - Michael De Vlieger, Feb 07 2026

Example

From Michael De Vlieger, Feb 07 2026: (Start)
Table of n, a(n) for n = 0..5:
n       a(n)
---------------------------------------------------------
0:        1   (empty product)
1:        6 = 2 * 3
2:      105 =     3 * 5 * 7
3:     5005 =         5 * 7 * 11 * 13
4:   323323 =             7 * 11 * 13 * 17 * 19
5: 30808063 =                 11 * 13 * 17 * 19 * 23 * 29 (End)

Mathematica

{1}~Join~Array[Times @@ Prime[Range @@ {#, 2 #}] &, 16] (* Michael De Vlieger, Feb 07 2026 *)

Prog

(PARI) a(n) = prod(k=n, 2*n, prime(k));

Crossrefs

Cf. A000040 (primes), A002110 (primorials), A051162.

Sequence in context: A126467 A013294 A013300 * A109819 A162130 A048707

Adjacent sequences: A330766 A330767 A330768 * A330770 A330771 A330772

Keyword

nonn

Author

Michel Marcus, Dec 30 2019

Status

approved