%I #12 Nov 01 2017 12:25:29

%S 1,7,43,371,3431,34153,353333,3770475,41165305,457714497,5164908167,

%T 58997692301,680874861687,7926902673655,92986983743513,

%U 1097999648804923,13040634990748733,155677447454317639,1866995100779692627,22482675584863229261

%N Number of n-bead necklaces labeled with numbers -6..6 not allowing reversal, with sum zero.

%H Andrew Howroyd, <a href="/A208595/b208595.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * A201550(d). - _Andrew Howroyd_, Mar 02 2017

%e Some solutions for n=4:

%e .-4...-5...-4...-6...-5...-3...-4...-1...-4...-6...-6...-4...-6...-1...-5...-4

%e ..4....2...-3....5....0....1....0....0....2...-1....3....2....5...-1....4....2

%e ..0...-1....4....1....0....2...-1....0...-3....1....2...-2...-4....0....2....4

%e ..0....4....3....0....5....0....5....1....5....6....1....4....5....2...-1...-2

%t comps[r_, m_, k_] := Sum[(-1)^i*Binomial[r - 1 - i*m, k - 1]*Binomial[k, i], {i, 0, Floor[(r - k)/m]}]; a[n_Integer, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] = a[n, 6]; Array[a, 20] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)

%Y Column 6 of A208597.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 29 2012

%E a(15)-a(20) from _Andrew Howroyd_, Mar 02 2017