This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259633 #27 Sep 01 2015 16:56:13 %S A259633 1,1,1,2,1,12,1,43,132,547,1,7834,1,30442,608887,3834978,1,84536629,1, %T A259633 3030450058,79538220753,16701983083,1,4136127573912,26625599501697, %U A259633 2730194738935 %N 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. %C A259633 "Equivalence" refers to the cyclic group. Turning over is not allowed. %C A259633 The original definition referred to slices of pie with slices of size 1/i, which add to a full pie. %F A259633 a(p) = 1 for all primes. %e A259633 a(6) = 12 because a pie can be made in the following twelve ways (moving clockwise from a 1/6): %e A259633 1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6, %e A259633 1 = 1/6 + 1/6 + 1/6 + 1/4 + 1/4, %e A259633 1 = 1/6 + 1/6 + 1/4 + 1/6 + 1/4, %e A259633 1 = 1/6 + 1/4 + 1/4 + 1/3, %e A259633 1 = 1/6 + 1/4 + 1/3 + 1/4, %e A259633 1 = 1/6 + 1/3 + 1/4 + 1/4, %e A259633 1 = 1/6 + 1/6 + 1/6 + 1/2, %e A259633 1 = 1/6 + 1/6 + 1/6 + 1/6 + 1/3, %e A259633 1 = 1/6 + 1/6 + 1/3 + 1/3, %e A259633 1 = 1/6 + 1/3 + 1/6 + 1/3, %e A259633 1 = 1/6 + 1/3 + 1/2, %e A259633 1 = 1/6 + 1/2 + 1/3. %e A259633 Notice that the bottom two pies are chiral copies of one another. %Y A259633 Cf. A092666. %K A259633 nonn,more %O A259633 1,4 %A A259633 _Gordon Hamilton_, Jul 02 2015 %E A259633 a(6) corrected, a(8) confirmed, a(9)-a(17) added by _Alois P. Heinz_, Jul 28 2015 %E A259633 a(18)-a(23) from _Alois P. Heinz_, Jul 30 2015 %E A259633 a(24)-a(26) from _Alois P. Heinz_, Sep 01 2015