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A072472
a(n) = product of numbers from prime(n)+1 up to prime(n+1), where prime(n) is the n-th prime.
6
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
1,1
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
LINKS
FORMULA
a(n) = A000040(n+1)*A061214(n). - Karl-Heinz Hofmann, Apr 18 2023
EXAMPLE
a(1) = 3
a(2) = 4 * 5 = 20
a(3) = 6 * 7 = 42
a(4) = 8 * 9 * 10 * 11 = 7920
MATHEMATICA
a[n_] := Product[k, {k, Prime[n] + 1, Prime[n + 1]}]; Table[a[n], {n, 1, 30}]
PROG
(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
(PARI) a(n) = prod(k=prime(n)+1, prime(n+1), k); \\ Michel Marcus, Apr 17 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 20 2002
EXTENSIONS
Edited by Robert G. Wilson v, Jun 21 2002
Offset, data and name corrected by Karl-Heinz Hofmann, Apr 18 2023
STATUS
approved