A084762 Numerator of Product_{2 <= p < 2*n} (2*n - p)/p.

1, 1, 1, 1, 1, 3, 9, 9, 5, 27, 135, 7, 567, 3375, 45, 54675, 1215, 25, 13395375, 168399, 1625, 4975425, 164025, 13125, 5373459, 1031443875, 145775, 2015047125, 5367718125, 931, 377950505625, 644126175, 4501875

Offset

1,6

Links

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

Index entries for sequences related to Goldbach conjecture

Formula

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

Example

The first terms of a(n)/A084763(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

A084762[n_]:= Numerator[Product[(2*n -Prime[j])/Prime[j], {j, 2, PrimePi[2*n] }]];
Table[A084762[n], {n, 40}] (* G. C. Greubel, May 16 2023 *)

Prog

(Magma)
A084762:= func< n | n eq 1 select 1 else Numerator(&*[(2*n - NthPrime(j))/NthPrime(j): j in [2..#PrimesUpTo(2*n)]]) >;
[A084762(n): n in [1..40]]; // G. C. Greubel, May 16 2023
(SageMath)
def A084762(n): return numerator(product((2*n-j)/j for j in prime_range(3, 2*n) ))
[A084762(n) for n in range(1, 40)] # G. C. Greubel, May 16 2023

Crossrefs

Cf. A000040, A000720, A084763 (denominators).

Sequence in context: A091559 A268107 A306963 * A188444 A372914 A201409

Adjacent sequences: A084759 A084760 A084761 * A084763 A084764 A084765

Keyword

nonn,frac

Author

Reinhard Zumkeller, Jun 03 2003

Status

approved