A107754 Number of subsets of the n-th roots of unity that sum to 1.

1, 1, 1, 2, 1, 6, 1, 8, 4, 18, 1, 60, 1, 66, 20, 128, 1, 600, 1, 612, 68, 1026, 1, 6000, 16, 4098, 256, 8580, 1, 95226, 1, 32768

Offset: 1

Author

T. D. Noe, May 23 2005

Keywords

• nonn
• more

Crossrefs

Cf. A103314 (number of subsets of the n-th roots of unity summing to zero) and A108417 (number of subsets of the n-th roots of unity summing to the absolute value of 1).

Programs

Mathematica

<< DiscreteMath`Combinatorica`; f[n_] := Plus @@ Table[ Count[ KSubsets[ Range[n], k], q_List /; Chop[ -1 + Plus @@ (E^((2.*Pi*I*q)/n))] === 0], {k, 0, n}]; Table[ f[n], {n, 24}] (* Robert G. Wilson v, Jun 03 2005 *)

Formula

For prime p, a(p^i) = 2^(p^(i-1)-1).