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

0, 0, 1, 0, 1, 9, 1, 0, 74, 33, 1, 1170, 1, 129, 15101, 0, 1, 187758, 1, 67650, 615700, 2049, 1, 4793490, 3247204, 8193, 262658, 4227330, 1, 480000312, 1, 0, 2458463380, 131073, 10787055277, 19903096980, 1, 524289, 67117058, 567489872400, 1, 2686322969514, 1

Offset: 1

Author

Michel Marcus, Nov 26 2012

Keywords

• nonn

Comments

E. Vantieghem proved that a(n) = 1 if and only if n is an odd prime. - Michel Marcus, Nov 26 2012

Links

• E. Vantieghem, On a congruence only holding for primes II, arXiv:0812.2841 [math.NT], 2008-2009.

Crossrefs

Cf. A028362.

Programs

Mathematica

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 *)

PARI

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

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

Formula

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