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%I #21 Nov 01 2017 12:23:56
%S 1,1,2,24,204,2635,39990,720916,14913192,348684381,9090909090,
%T 261535848376,8230246567620,281241174889207,10371206370593250,
%U 410525522392242720,17361641481138401520,781282469565908953017,37275544492386193492506,1879498672877604463254424
%N Number of n-bead necklaces of n colors not allowing reversal, with no adjacent beads having the same color.
%H Andrew Howroyd, <a href="/A208533/b208533.txt">Table of n, a(n) for n = 1..80</a>
%F a(n) = (1/n) * Sum_{d | n} totient(n/d) * ((n-1)*(-1)^d + (n-1)^d) for n > 1. - _Andrew Howroyd_, Mar 12 2017
%e All solutions for n=4:
%e ..2....1....1....1....1....1....2....1....1....3....1....1....1....2....1....1
%e ..3....2....4....4....4....3....4....4....3....4....3....4....2....3....2....2
%e ..2....4....2....3....2....2....3....1....1....3....4....3....1....4....3....1
%e ..4....2....4....2....3....3....4....4....3....4....2....4....4....3....2....2
%e ..
%e ..1....1....2....1....2....1....1....1
%e ..2....3....3....3....4....2....2....3
%e ..1....4....2....1....2....4....3....2
%e ..3....3....3....4....4....3....4....4
%t a[1] = 1; a[n_] = (1/n)*DivisorSum[n, EulerPhi[n/#]*((n-1)*(-1)^# + (n-1)^#)& ]; Array[a, 20] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)
%o (PARI) a(n) = if (n==1, 1, (1/n) * sumdiv(n, d, eulerphi(n/d) * ((n-1)*(-1)^d + (n-1)^d))); \\ _Michel Marcus_, Nov 01 2017
%Y Diagonal of A208535.
%K nonn
%O 1,3
%A _R. H. Hardin_, Feb 27 2012
%E a(14)-a(20) from _Andrew Howroyd_, Mar 12 2017
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