|
%I #27 Sep 01 2015 16:56:13
%S 1,1,1,2,1,12,1,43,132,547,1,7834,1,30442,608887,3834978,1,84536629,1,
%T 3030450058,79538220753,16701983083,1,4136127573912,26625599501697,
%U 2730194738935
%N 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.
%C "Equivalence" refers to the cyclic group. Turning over is not allowed.
%C The original definition referred to slices of pie with slices of size 1/i, which add to a full pie.
%F a(p) = 1 for all primes.
%e a(6) = 12 because a pie can be made in the following twelve ways (moving clockwise from a 1/6):
%e 1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6,
%e 1 = 1/6 + 1/6 + 1/6 + 1/4 + 1/4,
%e 1 = 1/6 + 1/6 + 1/4 + 1/6 + 1/4,
%e 1 = 1/6 + 1/4 + 1/4 + 1/3,
%e 1 = 1/6 + 1/4 + 1/3 + 1/4,
%e 1 = 1/6 + 1/3 + 1/4 + 1/4,
%e 1 = 1/6 + 1/6 + 1/6 + 1/2,
%e 1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/3,
%e 1 = 1/6 + 1/6 + 1/3 + 1/3,
%e 1 = 1/6 + 1/3 + 1/6 + 1/3,
%e 1 = 1/6 + 1/3 + 1/2,
%e 1 = 1/6 + 1/2 + 1/3.
%e Notice that the bottom two pies are chiral copies of one another.
%Y Cf. A092666.
%K nonn,more
%O 1,4
%A _Gordon Hamilton_, Jul 02 2015
%E a(6) corrected, a(8) confirmed, a(9)-a(17) added by _Alois P. Heinz_, Jul 28 2015
%E a(18)-a(23) from _Alois P. Heinz_, Jul 30 2015
%E a(24)-a(26) from _Alois P. Heinz_, Sep 01 2015
| 