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A008555
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Primitive parts of Pell numbers.
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10
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1, 2, 5, 6, 29, 7, 169, 34, 197, 41, 5741, 33, 33461, 239, 1345, 1154, 1136689, 199, 6625109, 1121, 45697, 8119, 225058681, 1153, 45232349, 47321, 7761797, 38081, 44560482149, 961, 259717522849, 1331714, 52734529, 1607521, 1800193921, 39201
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OFFSET
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1,2
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COMMENTS
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Also called Sylvester-Pell cyclotomic numbers. - Paul Barry, Apr 15 2005
According to Guy, Raphael Robinson noticed that a(7) and a(30) are squares and asked if there are more. There are no others in the first 10000 terms. [T. D. Noe, May 07 2009]
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, A3.
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LINKS
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FORMULA
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a(n) = Product_{k=1..n-1} if(gcd(n, k)=1, (1+sqrt(2))-(1-sqrt(2))*exp(2*Pi*I*k/n), 1), I=sqrt(-1). - Paul Barry, Apr 15 2005
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EXAMPLE
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a(8)=34 because pell(8)=408 and 408/(a(4)*a(2)*a(1)) = 408/12 = 34. [From T. D. Noe, May 07 2009]
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MATHEMATICA
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pell={1, 2}; pp={1, 2}; Do[s=2*pell[[ -1]]+pell[[ -2]]; AppendTo[pell, s]; AppendTo[pp, s/Times@@pp[[Most[Divisors[n]]]]], {n, 3, 40}]; pp (* T. D. Noe, May 07 2009 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended by T. D. Noe, May 07 2009
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STATUS
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approved
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