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

1,3

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.

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

Crossrefs

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

Sequence in context: A129738 A271314 A292006 * A264987 A170835 A122133

Adjacent sequences: A105600 A105601 A105602 * A105604 A105605 A105606

Keyword

easy,nonn

Author

Paul Barry, Apr 15 2005

Status

approved