

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
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OFFSET

1,2


COMMENTS

Also called SylvesterPell 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. [From T. D. Noe, May 07 2009]


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, A3.


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number.  Paul Barry, Apr 15 2005


FORMULA

a(n) = A000129(n) / product_{d<n,dn} a(d) [From T. D. Noe, May 07 2009]
a(n)=product{k=1..n1, if(gcd(n, k)=1, (1+sqrt(2))(1sqrt(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 [From T. D. Noe, May 07 2009]


CROSSREFS

Cf. A061446 (primitive part of Fibonacci numbers) [From T. D. Noe, May 07 2009]
Cf. A105606.
Sequence in context: A137067 A214200 A273924 * A056441 A164805 A275285
Adjacent sequences: A008552 A008553 A008554 * A008556 A008557 A008558


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Corrected and extended by T. D. Noe, May 07 2009
Edited by N. J. A. Sloane, Oct 04 2009


STATUS

approved



