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A008555
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Primitive parts of Pell numbers.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also called Sylvester-Pell cyclotomic numbers. - Paul Barry (pbarry(AT)wit.ie), 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. [From T. D. Noe (noe(AT)sspectra.com), May 07 2009]
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, A3.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number. - Paul Barry (pbarry(AT)wit.ie), Apr 15 2005
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FORMULA
| a(n) = A000129(n) / product_{d<n,d|n} a(d) [From T. D. Noe (noe(AT)sspectra.com), May 07 2009]
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 (pbarry(AT)wit.ie), Apr 15 2005
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EXAMPLE
| a(8)=34 because pell(8)=408 and 408/(a(4)*a(2)*a(1)) = 408/12 = 34. [From T. D. Noe (noe(AT)sspectra.com), May 07 2009]
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MATHEMATICA
| 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 [From T. D. Noe (noe(AT)sspectra.com), May 07 2009]
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CROSSREFS
| Cf. A061446 (primitive part of Fibonacci numbers) [From T. D. Noe (noe(AT)sspectra.com), May 07 2009]
Cf. A105606.
Sequence in context: A128367 A178924 A137067 * A056441 A164805 A152918
Adjacent sequences: A008552 A008553 A008554 * A008556 A008557 A008558
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by T. D. Noe (noe(AT)sspectra.com), May 07 2009
Edited by N. J. A. Sloane, Oct 04 2009
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