

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. [T. D. Noe, May 07 2009]


REFERENCES

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


LINKS



FORMULA

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 (* T. D. Noe, May 07 2009 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Corrected and extended by T. D. Noe, May 07 2009


STATUS

approved



