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A008555 Primitive parts of Pell numbers. 10
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; text; internal format)
OFFSET
1,2
COMMENTS
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]
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, A3.
LINKS
Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number. - Paul Barry, Apr 15 2005
FORMULA
a(n) = A000129(n) / Product_{d<n,d|n} a(d). [T. D. Noe, 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, Apr 15 2005
EXAMPLE
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]
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 (* T. D. Noe, May 07 2009 *)
CROSSREFS
Cf. A061446 (primitive part of Fibonacci numbers). [T. D. Noe, May 07 2009]
Cf. A105606.
Sequence in context: A137067 A214200 A273924 * A056441 A365085 A164805
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended by T. D. Noe, May 07 2009
Edited by N. J. A. Sloane, Oct 04 2009
STATUS
approved

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Last modified February 28 02:18 EST 2024. Contains 370379 sequences. (Running on oeis4.)