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A259633
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a(n) = number of inequivalent necklaces with beads labeled 1/i (1 <= i <= n) such that the sum of the beads is 1 and the smallest bead is 1/n.
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1
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1, 1, 1, 2, 1, 12, 1, 43, 132, 547, 1, 7834, 1, 30442, 608887, 3834978, 1, 84536629, 1, 3030450058, 79538220753, 16701983083, 1, 4136127573912, 26625599501697, 2730194738935
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OFFSET
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1,4
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COMMENTS
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"Equivalence" refers to the cyclic group. Turning over is not allowed.
The original definition referred to slices of pie with slices of size 1/i, which add to a full pie.
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LINKS
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FORMULA
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a(p) = 1 for all primes.
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EXAMPLE
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a(6) = 12 because a pie can be made in the following twelve ways (moving clockwise from a 1/6):
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6,
1 = 1/6 + 1/6 + 1/6 + 1/4 + 1/4,
1 = 1/6 + 1/6 + 1/4 + 1/6 + 1/4,
1 = 1/6 + 1/4 + 1/4 + 1/3,
1 = 1/6 + 1/4 + 1/3 + 1/4,
1 = 1/6 + 1/3 + 1/4 + 1/4,
1 = 1/6 + 1/6 + 1/6 + 1/2,
1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/3,
1 = 1/6 + 1/6 + 1/3 + 1/3,
1 = 1/6 + 1/3 + 1/6 + 1/3,
1 = 1/6 + 1/3 + 1/2,
1 = 1/6 + 1/2 + 1/3.
Notice that the bottom two pies are chiral copies of one another.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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a(6) corrected, a(8) confirmed, a(9)-a(17) added by Alois P. Heinz, Jul 28 2015
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STATUS
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approved
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