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 A002348 Degree of rational Poncelet porism of n-gon. (Formerly M0549 N0198) 2
 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; refs; listen; history; text; internal format)
 OFFSET 3,2 REFERENCES Kerawala, S. M.; Poncelet Porism in Two Circles. Bull. Calcutta Math. Soc. 39, 85-105, 1947. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 3..10000 Eric Weisstein's World of Mathematics, Poncelet's Porism EXAMPLE For a triangle the degree is 1, thus a(3) = 1. - Michael Somos, Dec 07 2018 MATHEMATICA 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 ] ] PROG (PARI) {a(n) = my(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 */ (Haskell) a002348 n = product (zipWith d ps es) * 4 ^ e0 `div` 8 where    d p e = (p ^ 2 - 1) * p ^ e    e0 = if even n then head \$ a124010_row n else 0    es = map ((* 2) . subtract 1) \$             if even n then tail \$ a124010_row n else a124010_row n    ps = if even n then tail \$ a027748_row n else a027748_row n -- Reinhard Zumkeller, Mar 18 2012 CROSSREFS Cf. A027748, A124010. Sequence in context: A097273 A006446 A261342 * A019469 A081491 A048716 Adjacent sequences:  A002345 A002346 A002347 * A002349 A002350 A002351 KEYWORD nonn,nice AUTHOR EXTENSIONS Extended with Mathematica program by Eric W. Weisstein STATUS approved

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Last modified June 16 19:43 EDT 2019. Contains 324155 sequences. (Running on oeis4.)