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Search: id:A107861
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| A107861 |
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Number of unique values in the sums of all subsets of the n-th roots of unity. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 David W. Wilson's conjectured formula for A103314 may apply to this sequence also. Observe that due to symmetry, n divides a(n)-1.
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LINKS
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T. D. Noe, Sums of Roots of Unity Plots
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EXAMPLE
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a(1)=2 as there are two distinct sums: the sum of empty subset of roots is 0 and the sum of {1} is 1.
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PROGRAM
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{ a(n) = local(S=Set()); forvec(c=vector(n, i, [0, 1]), S=setunion(S, [Pol(c)%polcyclo(n)])); length(S) } (Max Alekseyev)
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CROSSREFS
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Cf. A103314 (number of subsets of the n-th roots of unity summing to zero).
Adjacent sequences: A107858 A107859 A107860 this_sequence A107862 A107863 A107864
Sequence in context: A057239 A024541 A123481 this_sequence A109800 A152136 A059180
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 25 2005
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EXTENSIONS
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a(1) corrected by Max Alekseyev, Jun 25 2007
a(21)-a(32) from Max Alekseyev (maxale(AT)gmail.com), Sep 07 2007
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