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A219732 a(n) = (Prod_{1 <= i <= n-1} (2^i + 1)) modulo (2^n - 1). 1

%I

%S 0,0,1,0,1,9,1,0,74,33,1,1170,1,129,15101,0,1,187758,1,67650,615700,

%T 2049,1,4793490,3247204,8193,262658,4227330,1,480000312,1,0,

%U 2458463380,131073,10787055277,19903096980,1,524289,67117058,567489872400,1,2686322969514,1

%N a(n) = (Prod_{1 <= i <= n-1} (2^i + 1)) modulo (2^n - 1).

%C E. Vantieghem proved that a(n) = 1 if and only if n is an odd prime. - _Michel Marcus_, Nov 26 2012

%H E. Vantieghem, <a href="http://arxiv.org/abs/0812.2841">On a congruence only holding for primes II</a>, arXiv:0812.2841

%F a(n) = A028362(n) modulo (2^n - 1).

%t Join[{0}, Table[m = 2^n - 1; prod = 1; Do[prod = Mod[prod*(2^i + 1), m], {i, n - 1}]; prod, {n, 2, 40}]] (* _T. D. Noe_, Nov 27 2012 *)

%o (PARI) a(m) = {for (n=1, m, print1(prod(j=1, n-1, 2^j+1) % (2^n - 1), ", "););}

%o (PARI) a(n)=if(n>2,my(m=2^n-1);lift(prod(i=1,n-1,Mod(2,m)^i+1)),0) \\ _Charles R Greathouse IV_, Nov 26 2012

%Y Cf. A028362.

%K nonn

%O 1,6

%A _Michel Marcus_, Nov 26 2012

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)