OFFSET
1,1
COMMENTS
Note that a(6)=19, a(12)=19^2 and a(18)=19^3. Similarly, a(10)=211 and a(20)=211^2. For prime n, a(n)=2^n-1. For powers of 2, we have a(2^n)=3^(2^(n-1)). It appears that David W. Wilson's conjectured formula for A103314 may apply to this sequence also. Observe that due to symmetry, n divides a(n)-1.
Definition edited by N. J. A. Sloane, Apr 09 2020. The old definition was "Number of unique values in the sums of all subsets of the n-th roots of unity".
LINKS
EXAMPLE
a(1)=2 as there are two distinct sums: the sum of the empty subset of roots is 0, and the sum of {1} is 1.
PROG
(PARI) { a(n) = my(S=Set()); forvec(c=vector(n, i, [0, 1]), S=setunion(S, [Pol(c)%polcyclo(n)])); #S } /* Max Alekseyev, Jun 25 2007 */
CROSSREFS
KEYWORD
nonn,more
AUTHOR
T. D. Noe, May 25 2005
EXTENSIONS
a(1) corrected by Max Alekseyev, Jun 25 2007
a(21)-a(32) from Max Alekseyev, Sep 07 2007
STATUS
approved