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A164896
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Number of subsets (up to cyclic shifts) of the n-th roots of 1 with zero sum.
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2
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1, 2, 2, 3, 2, 5, 2, 6, 4, 9, 2, 19, 2, 21, 10, 36, 2, 94, 2, 117, 22, 189, 2, 618, 8, 633, 60, 1203, 2, 6069, 2, 4116, 190, 7713, 26, 35324, 2, 27597, 634, 59706, 2, 328835, 2, 190935, 2728, 364725, 2, 2435780, 20, 1579884, 7714, 2582061, 2, 21013770, 194, 9894294, 27598, 18512793, 2, 377367015, 2, 69273669, 104832, 134219796, 638, 1678410951
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OFFSET
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1,2
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COMMENTS
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Cyclic shifts correspond to multiplication by a root of unity.
a(n)=2 for n prime, corresponding to the empty and the full subset. [Joerg Arndt, Jun 10 2011]
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LINKS
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Table of n, a(n) for n=1..66.
Joerg Arndt, Matters Computational (The Fxtbook), section 18.4 "Sums of roots of unity that are zero", p.383
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FORMULA
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a(n) = A110981(n) + sum_{d|n,d<n} A001037(d) = A110981(n) + A000031(n) - A001037(n). - Max Alekseyev, Apr 08 2013
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EXAMPLE
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a(6) = 5 because these subsets add to zero: (left: as bitstring, right: subset)
...... (empty sum)
..1..1 0 3
.1.1.1 0 2 4
.11.11 0 1 3 4
111111 0 1 2 3 4 5 (all roots of unity)
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CROSSREFS
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Cf. A103314, A110981 (counts subsets with bitstrings being Lyndon words).
Sequence in context: A328673 A115119 A066656 * A298422 A304716 A237984
Adjacent sequences: A164893 A164894 A164895 * A164897 A164898 A164899
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KEYWORD
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nonn
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AUTHOR
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Joerg Arndt, Aug 30 2009
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EXTENSIONS
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Added terms a(32)..a(39), Joerg Arndt, Jun 10 2011.
Terms a(40) onward from Max Alekseyev, Apr 08 2013
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STATUS
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approved
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