Search: id:A008555
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%I A008555
%S A008555 1,2,5,6,29,7,169,34,197,41,5741,33,33461,239,1345,1154,1136689,199,
%T A008555 6625109,1121,45697,8119,225058681,1153,45232349,47321,7761797,38081,
%U A008555 44560482149,961,259717522849,1331714,52734529,1607521,1800193921,39201
%N A008555 Primitive parts of Pell numbers.
%C A008555 Also called Sylvester-Pell cyclotomic numbers. - Paul Barry (pbarry(AT)wit.ie), 
               Apr 15 2005
%C A008555 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]
%D A008555 R. K. Guy, Unsolved Problems in Number Theory, A3.
%H A008555 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SylvesterCyclotomicNumber.html">Sylvester Cyclotomic Number</a>. 
               - Paul Barry (pbarry(AT)wit.ie), Apr 15 2005
%F A008555 a(n) = A000129(n) / product_{d<n,d|n} a(d) [From T. D. Noe (noe(AT)sspectra.com), 
               May 07 2009]
%F A008555 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
%e A008555 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]
%t A008555 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]
%Y A008555 Cf. A061446 (primitive part of Fibonacci numbers) [From T. D. Noe (noe(AT)sspectra.com), 
               May 07 2009]
%Y A008555 Cf. A105606.
%Y A008555 Sequence in context: A136324 A128367 A137067 this_sequence A056441 A164805 
               A152918
%Y A008555 Adjacent sequences: A008552 A008553 A008554 this_sequence A008556 A008557 
               A008558
%K A008555 nonn
%O A008555 1,2
%A A008555 N. J. A. Sloane (njas(AT)research.att.com).
%E A008555 Corrected and extended by T. D. Noe (noe(AT)sspectra.com), May 07 2009
%E A008555 Edited by N. J. A. Sloane, Oct 04 2009

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