A105603 Sylvester-Jacobsthal cyclotomic numbers.

1, 1, 3, 5, 11, 7, 43, 17, 57, 31, 683, 13, 2731, 127, 331, 257, 43691, 73, 174763, 205, 5419, 2047, 2796203, 241, 1016801, 8191, 261633, 3277, 178956971, 151, 715827883, 65537, 1397419, 131071, 24214051, 4033, 45812984491, 524287, 22366891, 61681

Offset: 1

Author

Paul Barry, Apr 15 2005

Keywords

• easy
• nonn

Comments

Primitive parts of Jacobsthal numbers A001045.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number.

Crossrefs

Cf. A020501, A001045, A061446 (with references), A008555.

Formula

a(n)=product{k=1..n-1, if(gcd(n, k)=1, 2+exp(2*pi*I*k/n), 1)}, I=sqrt(-1)

a(n) = (-1)^phi(n)*cyclotomic(n, -2) for n >= 2 (for n = 1 this would be 3), with phi(n) = A000010(n). - Wolfdieter Lang, Jan 19 2015