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A121773
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Number of n-bead necklaces with n+1 colors for n>0, with a(0)=1.
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1
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1, 2, 6, 24, 165, 1560, 19684, 299600, 5381685, 111111340, 2593758618, 67546215528, 1941507500933, 61054982558024, 2085209014017960, 76861433640597376, 3041324492665174641, 128583032925805678368, 5784852794346334629910, 275941052631578947368440
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (1/n)*Sum_{d|n} phi(n/d)*(n+1)^d, for n>0, with a(0)=1.
a(n) is divisible by (n+1); a(n)/(n+1) = A121774(n).
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MATHEMATICA
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a[0] = 1; a[n_] := DivisorSum[n, (n+1)^# * EulerPhi[n/#] &] / n; Array[a, 20, 0] (* Amiram Eldar, Aug 15 2023 *)
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PROG
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(PARI) a(n)=if(n==0, 1, (1/n)*sumdiv(n, d, eulerphi(n/d)*(n+1)^d))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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