

A259633


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.


1



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

1,4


COMMENTS

"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.


LINKS

Table of n, a(n) for n=1..26.


FORMULA

a(p) = 1 for all primes.


EXAMPLE

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.


CROSSREFS

Cf. A092666.
Sequence in context: A072512 A271531 A118588 * A174500 A249163 A287977
Adjacent sequences: A259630 A259631 A259632 * A259634 A259635 A259636


KEYWORD

nonn,more


AUTHOR

Gordon Hamilton, Jul 02 2015


EXTENSIONS

a(6) corrected, a(8) confirmed, a(9)a(17) added by Alois P. Heinz, Jul 28 2015
a(18)a(23) from Alois P. Heinz, Jul 30 2015
a(24)a(26) from Alois P. Heinz, Sep 01 2015


STATUS

approved



