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0, 0, 2, 2, 3, 2, 5, 2, 6, 4, 9, 2, 17, 2, 21, 10, 36, 2, 70, 2, 111, 22, 189, 2, 382, 8, 633, 60, 1185, 2, 2301, 2, 4116, 190, 7713, 26, 14940, 2, 27597, 634, 52518, 2, 101051, 2, 190749, 2248, 364725, 2, 703332, 20, 1342284, 7714, 2581431, 2, 4985610, 194
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OFFSET
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0,3
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COMMENTS
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This is the number of imprimitive (periodic) n-bead necklaces with 2 colors when turning over is not allowed. a(p)=2 for prime p. Presumably, a(n)=2*A115118(n) for odd n. - Valery A. Liskovets, Jan 17 2006
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LINKS
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FORMULA
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a(0) = 0; a(n) = (1/n)*Sum_{d|n} (phi(d)*2^(n/d) - mu(n/d)*2^d). [corrected by Michel Marcus, May 25 2022]
G.f.: Sum_{i>=1} (mu(i) - phi(i))*log(1 - 2*x^i)/i. - Herbert Kociemba, Nov 25 2016
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MATHEMATICA
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mx=40; f[x_]:=Sum[(MoebiusMu[i]-EulerPhi[i])Log[1-2*x^i]/i, {i, 1, mx}];
CoefficientList[Series[f[x], {x, 0, mx}], x] (* Herbert Kociemba, Nov 25 2016 *)
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PROG
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(PARI) a(n) = if (n==0, 0, sumdiv(n, d, (eulerphi(d)*2^(n/d) - moebius(n/d)*2^d))/n); \\ Michel Marcus, May 25 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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