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%I
%S 1,3,13,125,1761,34153,833253,24627705,855798877,34223775091,
%T 1549090700059,78325577416281,4376902102440375,267933660979057571,
%U 17834397187887850661,1282662234529669344753,99133711906097886767313,8194555387462964814207631
%N Number of n-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
%H Andrew Howroyd, <a href="/A208590/b208590.txt">Table of n, a(n) for n = 1..80</a>
%e All solutions for n=3:
%e .-2...-1...-2...-3...-3...-2....0...-1...-1...-2...-3...-3...-2
%e ..0....1....3....2....1....1....0....0...-1....2....0....3...-1
%e ..2....0...-1....1....2....1....0....1....2....0....3....0....3
%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_, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] := a[n, n]; Array[a, 18] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)
%Y Diagonal of A208597.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 29 2012
%E a(12)-a(18) from _Andrew Howroyd_, Mar 02 2017
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