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Number of primitive (=aperiodic) n-bead necklaces with colored beads of exactly 7 different colors.
2

%I #6 Jan 25 2015 10:16:56

%S 720,17640,258720,2963520,29317680,263506320,2215825920,17758540440,

%T 137337087888,1033793011440,7621696948320,55289495222640,

%U 396017903136240,2808175618022544,19754629731587280,138087381577881960,960370246763096400,6652267408747194360

%N Number of primitive (=aperiodic) n-bead necklaces with colored beads of exactly 7 different colors.

%H Alois P. Heinz, <a href="/A254079/b254079.txt">Table of n, a(n) for n = 7..1000</a>

%p with(numtheory):

%p b:= proc(n, k) option remember; `if`(n=0, 1,

%p add(mobius(n/d)*k^d, d=divisors(n))/n)

%p end:

%p a:= n-> add(b(n, 7-j)*binomial(7, j)*(-1)^j, j=0..7):

%p seq(a(n), n=7..30);

%Y Column k=7 of A254040.

%K nonn

%O 7,1

%A _Alois P. Heinz_, Jan 25 2015