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A057741
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Table T(n,k) giving number of elements of order k in dihedral group D_{2n} of order 2n, n >= 1, 1<=k<=g(n), where g(n) = 2 if n=1 else g(n) = n.
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2
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1, 1, 1, 3, 1, 3, 2, 1, 5, 0, 2, 1, 5, 0, 0, 4, 1, 7, 2, 0, 0, 2, 1, 7, 0, 0, 0, 0, 6, 1, 9, 0, 2, 0, 0, 0, 4, 1, 9, 2, 0, 0, 0, 0, 0, 6, 1, 11, 0, 0, 4, 0, 0, 0, 0, 4, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 13, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 1, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1, 15, 0, 0, 0, 0, 6, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Note that D_2 equals the cyclic group of order 2.
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FORMULA
| If k<>2 and k does not divide n, this number is 0; if k<>2 and k divides n, this number is phi(k), where phi is the Euler totient function; if k=2, this number is n for odd n and n+1 for even n.
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EXAMPLE
| 1,1; 1,3; 1,3,2; 1,5,0,2; 1,5,0,0,4; ...
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CROSSREFS
| Cf. A057731, A054522, A057740.
Sequence in context: A099906 A047787 A102668 * A133571 A171899 A083208
Adjacent sequences: A057738 A057739 A057740 * A057742 A057743 A057744
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KEYWORD
| nonn,tabf,easy,nice
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AUTHOR
| Roger CUCULIERE (cuculier(AT)imaginet.fr), Oct 29 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Oct 30 2000
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