Search: id:A114536
Results 1-1 of 1 results found.

%I A114536
%S A114536 1,1,1,1,1,2,1,1,1,2,1,3,1,2,3,1,1,2,1,4,3,2,1,3,1,2,1,4,1,12,1,1,3,2,
               5,
%T A114536 4,1,2,3,5,1,12,1,4,5,2,1,6,1,2,3,4,1,2,5,7,3,2,1,54,1,2,7,1,5,12,1,4,
               3,
%U A114536 32,1,8,1,2,3,4,7,12,1,7,1,2,1,55,5,2,3,8,1,58,7,4,3,2,5,6,1,2,9,4,1,12
%N A114536 Let the height of a polynomial be the largest coefficient in absolute 
               value. Then a(n) is the maximal height of a divisor of x^n-1 with 
               integral coefficients.
%D A114536 Carl Pomerance and Nathan C. Ryan, "The maximal height of divisors of 
               x^n-1." (To appear in Illinois Journal of Mathematics)
%H A114536 Felipe Garcia H., <a href="http://fgarciah.bol.ucla.edu/Research/research.html">
               Research</a>.
%H A114536 Nathan C. Ryan, <a href="http://www.math.ucla.edu/~nathan/research.html">
               Research</a>.
%F A114536 a(n)=1 iff n=1 or n=p^k where p is a prime and k is a positive integer; 
               a(pq)=min{p,q} where p and q are distinct primes.
%e A114536 a(6)=2 since (x+1)(x^2+x+1)=x^3+2x^2+2x+1 divides x^6-1 and no other 
               divisor has a greater height.
%t A114536 cyc[n_] := cyc[n] = Cyclotomic[n, x]; f[n_] := Block[{sd = Rest@ Subsets@ 
               Divisors@ n, lst = {}, lmt = 2^DivisorSigma[0, n]}, For[i = 1, i 
               < lmt, i++, AppendTo[lst, Max@ Abs@ CoefficientList[ Expand[ Times 
               @@ (cyc[ # ] & /@ sd[[i]])], x]]]; Max@lst]; Array[f, 102] (* Robert 
               G. Wilson v *)
%Y A114536 Cf. A117215 (number of divisors of x^n-1 having the maximal height).
%Y A114536 Sequence in context: A025865 A085091 A052128 this_sequence A138010 A167204 
               A104306
%Y A114536 Adjacent sequences: A114533 A114534 A114535 this_sequence A114537 A114538 
               A114539
%K A114536 nonn,nice
%O A114536 1,6
%A A114536 Felipe Garcia (fgarciah(AT)ucla.edu), Feb 15 2006
%E A114536 Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Mar 01 
               2006

Search completed in 0.001 seconds