A072472 a(n) = product of numbers from prime(n)+1 up to prime(n+1), where prime(n) is the n-th prime.

3, 20, 42, 7920, 156, 57120, 342, 212520, 342014400, 930, 1673844480, 2430480, 1806, 4280760, 16529385600, 32441381280, 3660, 71852901120, 23319240, 5256, 200133133200, 44102880, 418397031360, 5827054819622400, 97990200, 10506, 123854640, 11772, 154529760

Offset: 1

Author

Amarnath Murthy, Jun 20 2002

Keywords

• nonn

Comments

Originally the offset was -1 and two terms more in front were pre defined in a inscrutable manner (a(-1)=1, a(0) = 2; .....). - Karl-Heinz Hofmann, Apr 18 2023

Examples

			a(1) = 3
a(2) = 4 * 5 = 20
a(3) = 6 * 7 = 42
a(4) = 8 * 9 * 10 * 11 = 7920
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A061214, A361760, A361761.

Programs

Mathematica

a[n_] := Product[k, {k, Prime[n] + 1, Prime[n + 1]}]; Table[a[n], {n, 1, 30}]

PARI

a(n) = prod(k=prime(n)+1, prime(n+1), k); \\ Michel Marcus, Apr 17 2023

Python

from sympy import prod, sieve as prime
def A072472(n):
    return prod(range(prime[n]+1, prime[n+1]+1)) # Karl-Heinz Hofmann, Apr 17 2023

Formula

a(n) = A000040(n+1)*A061214(n). - Karl-Heinz Hofmann, Apr 18 2023

Extensions

Edited by Robert G. Wilson v, Jun 21 2002

Offset, data and name corrected by Karl-Heinz Hofmann, Apr 18 2023