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
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) = 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
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