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, 2, 1, 12, 1, 43, 132, 547, 1, 7834, 1, 30442, 608887, 3834978, 1, 84536629, 1, 3030450058, 79538220753, 16701983083, 1, 4136127573912, 26625599501697, 2730194738935

Offset: 1

Author

Gordon Hamilton, Jul 02 2015

Keywords

• nonn
• more

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.

Examples

			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.

Formula

a(p) = 1 for all primes.

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