A084763 Denominator of Product_{ 2 <= p < 2*n } (2*n - p)/p.

1, 3, 5, 7, 1, 11, 65, 7, 17, 209, 91, 23, 187, 247, 29, 133331, 247, 1, 5454059, 7657, 697, 9263963, 21793, 14053, 464899, 15930683, 29203, 39844579, 21553277, 59, 153749947889, 18594017, 21607, 11579203541083, 3008581

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Goldbach conjecture

Formula

a(n) = denominator( Product_{j=2..A000720(2*n)} (2*n - prime(j) ) / prime(j) ). - G. C. Greubel, May 16 2023

Example

The first terms of A084762(n)/a(n): 1/1, 1/3, 1/5, 1/7, 1/1, 3/11, 9/65, 9/7, 5/17, 27/209, 135/91, 7/23, ...

Mathematica

A084763[n_]:= Denominator[Product[(2*n -Prime[j])/Prime[j], {j, 2, PrimePi[2*n] }]];
Table[A084763[n], {n, 40}] (* G. C. Greubel, May 16 2023 *)

Prog

(Magma)
A084763:= func< n | n eq 1 select 1 else Denominator(&*[(2*n - NthPrime(j))/NthPrime(j): j in [2..#PrimesUpTo(2*n)]]) >;
[A084763(n): n in [1..40]]; // G. C. Greubel, May 16 2023
(SageMath)
def A084763(n): return denominator(product((2*n-j)/j for j in prime_range(3, 2*n)))
[A084763(n) for n in range(1, 40)] # G. C. Greubel, May 16 2023

Crossrefs

Cf. A084762 (numerator).

Sequence in context: A021032 A212120 A128059 * A179650 A131214 A271833

Adjacent sequences: A084760 A084761 A084762 * A084764 A084765 A084766

Keyword

nonn,frac

Author

Reinhard Zumkeller, Jun 03 2003

Status

approved