login
a(n) = Product_{k=2..floor(sqrt(2n-1)/2)+1} (2n-1) mod (2k-1).
1

%I #32 Mar 03 2024 10:15:34

%S 1,1,2,1,0,2,1,0,4,4,0,6,0,0,8,1,0,0,4,0,12,3,0,20,0,0,24,0,0,24,5,0,

%T 0,32,0,16,9,0,0,56,0,72,0,0,320,0,0,0,84,0,24,240,0,512,160,0,90,0,0,

%U 0,0,0,0,12,0,500,0,0,160,672,0,0,0,0,2880,1792,0,0,72,0,0,378

%N a(n) = Product_{k=2..floor(sqrt(2n-1)/2)+1} (2n-1) mod (2k-1).

%C For n>1, if a(n) > 0 then 2n-1 is prime.

%C From _Robert G. Wilson v_, Mar 15 2017: (Start)

%C Except for n=1, a(n)=0 iff 2n-1 is not prime (A104275).

%C a(n) is prime for n: 3, 6, 22 & 31. (End)

%H Charles R Greathouse IV, <a href="/A283616/b283616.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[Product[Mod[(2 n - 1), (2 k - 1)], {k, 2, Floor[Sqrt[2 n - 1]/2] + 1}], {n, 80}] (* _Michael De Vlieger_, Mar 15 2017 *)

%o (PARI) a(n)=my(t=2*n-1); prod(k=2,sqrtint(t\4)+1, t%(2*k-1)) \\ _Charles R Greathouse IV_, Mar 22 2017

%Y Cf. A180491.

%K nonn

%O 1,3

%A _Zhandos Mambetaliyev_, Mar 11 2017