OFFSET
0,3
COMMENTS
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
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Randall L Rathbun, Jan 10 2002
STATUS
approved