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A107861
Number of distinct values taken by the sums of all subsets of the n-th roots of unity.
4
2, 3, 7, 9, 31, 19, 127, 81, 343, 211, 2047, 361, 8191, 2059, 14221, 6561, 131071, 6859, 524287, 44521, 778765, 175099, 8388607, 130321, 28629151, 1586131, 40353607, 4239481, 536870911, 1360291, 2147483647, 43046721
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".
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
Cf. A103314 (number of subsets of the n-th roots of unity summing to zero).
Sequence in context: A255393 A248037 A123481 * A109800 A152136 A059180
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