A238711 - OEIS

%I #12 Oct 04 2020 23:28:15

%S 2,3,15,105,35,231,2145,5005,4641,53295,1616615,119301,21505,7436429,

%T 21489,57998985,3038795305,4123,13844919,10393190665,12838371,

%U 299859855,7292509103495,12023917269,70691995,37198413949697,62483343,2769282065,98755025688454681

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

%C Product of n-th row in triangle A171637;

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

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

%C Product of the distinct primes in the Goldbach partitions of 2n. - _Wesley Ivan Hurt_, Sep 29 2020

%H Reinhard Zumkeller, <a href="/A238711/b238711.txt">Table of n, a(n) for n = 2..2000</a>

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

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

%F 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;

%F 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

%o (Haskell)

%o a238711 n = product $ filter ((== 1) . a010051') $

%o    map (2 * n -) $ takeWhile (<= 2 * n) a000040_list

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

%K nonn

%O 2,1

%A _Reinhard Zumkeller_, Mar 06 2014