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1, 4, 6, 8, 12, 12, 14, 24, 18, 20, 32, 24, 30, 36, 30, 32, 48, 48, 38, 56, 42, 44, 72, 48, 56, 72, 54, 72, 80, 60, 62, 96, 84, 68, 96, 72, 74, 120, 96, 80, 108, 84, 108, 120, 90, 112, 128, 120, 98, 144, 102, 104, 192, 108, 110, 152, 114, 144, 168, 144, 132, 168
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of coincidence site lattices of index 2n+1 in lattice Z^3.
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REFERENCES
| M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
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FORMULA
| Dirichlet series: Product (1+p^(-s))/(1-p^(1-s)); p != 2.
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MAPLE
| Contribution from Peter Luschny (peter(AT)luschny.de), Oct 23 2010: (Start)
A001615 := n -> mul((op(1, i)+1)*op(1, i)^(op(2, i)-1), i=op(2, numtheory[ifactors](n)));
A031359 := n -> A001615(2*n-1); (End)
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MATHEMATICA
| a[n_] := (2n-1)*Sum[ MoebiusMu[d]^2/d, {d, Divisors[2n-1]}]; Table[a[n], {n, 1, 62}] (* From Jean-François Alcover, Jan 18 2012, after Michael Somos *)
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CROSSREFS
| Sequence in context: A139404 A014455 A110646 * A179852 A110606 A117247
Adjacent sequences: A031356 A031357 A031358 * A031360 A031361 A031362
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 25 2002
More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 24 2002
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