A238711 Product of all primes p such that 2n - p is also prime.

2, 3, 15, 105, 35, 231, 2145, 5005, 4641, 53295, 1616615, 119301, 21505, 7436429, 21489, 57998985, 3038795305, 4123, 13844919, 10393190665, 12838371, 299859855, 7292509103495, 12023917269, 70691995, 37198413949697, 62483343, 2769282065, 98755025688454681

Offset: 2

Author

Reinhard Zumkeller, Mar 06 2014

Keywords

• nonn

Comments

Product of n-th row in triangle A171637;

All terms greater than 3 are odd, composite and squarefree numbers, cf. A024556.

n is prime iff n is a factor of a(n).

Product of the distinct primes in the Goldbach partitions of 2n. - Wesley Ivan Hurt, Sep 29 2020

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..2000

Crossrefs

Cf. A000040, A010051, A238778, subsequence of A056911.

Programs

Haskell

a238711 n = product $ filter ((== 1) . a010051') $
   map (2 * n -) $ takeWhile (<= 2 * n) a000040_list

Mathematica

Table[Times@@Select[Select[Prime[Range[2 n]], # < 2 n &], PrimeQ[2 n - #] &], {n, 2, 30}] (* Robert Price, Apr 26 2025 *)

Formula

A020639(a(n)) = A020481(n); A006530(a(n)) = A020482(n);

A001221(a(n)) = A035026(n); A008472(a(n)) = A238778(n);

A027748(a(n),k) + A027748(a(n),l+1-k) = 2*n for k=1..l, with l=A001221(a(n)); particulary A020639(a(n))+A006530(a(n)) = 2*n;

a(n) = n^c(n) * Product_{i=1..n-1} (i*(2*n-i))^(c(i)*c(2*n-i)), where c is the prime characteristic (A010051). - Wesley Ivan Hurt, Sep 29 2020