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Search: id:A002348
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| A002348 |
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Degree of rational Poncelet porism of n-gon.
(Formerly M0549 N0198)
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+0
1
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| 1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 21, 24, 24, 32, 36, 36, 45, 48, 48, 60, 66, 64, 75, 84, 81, 96, 105, 96, 120, 128, 120, 144, 144, 144, 171, 180, 168, 192, 210, 192, 231, 240, 216, 264, 276, 256, 294, 300, 288, 336, 351, 324, 360, 384, 360, 420, 435, 384, 465
(list; graph; listen)
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OFFSET
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3,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
Kerawala, S. M.; Poncelet Porism in Two Circles. Bull. Calcutta Math. Soc. 39, 85-105, 1947.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
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Poncelet[ n_Integer /; n >= 3 ] := Module[ {p, a, i}, {p, a}=Transpose[ FactorInteger[ n ] ];
If[ p[ [ 1 ] ]==2, 4^a[ [ 1 ] ]Product[ p[ [ i ] ]^(2(a[ [ i ] ]-1))(p[ [ i ] ]^2-1), {i, 2, Length[ p ]} ]/8, (* Else *) Product[ p[ [ i ] ]^(2(a[ [ i ] ]-1))(p[ [ i ] ]^2-1), {i, Length[ p ]} ]/8 ] ]
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PROGRAM
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(PARI) a(n)= local(p, e); if(n<3, 0, p=factor(n)~; e=p[2, ]; p=p[1, ]; if(p[1]==2, 4^e[1], 1)* prod(i=1+(p[1]==2), length(p), p[i]^(2*(e[i]-1))* (p[i]^2-1))/8) - Michael Somos, Dec 09 1999
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CROSSREFS
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Adjacent sequences: A002345 A002346 A002347 this_sequence A002349 A002350 A002351
Sequence in context: A033501 A097273 A006446 this_sequence A019469 A081491 A161826
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended with Mathematica program by Eric Weisstein (eric(AT)weisstein.com)
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