%I A088867
%S A088867 680914892583617,55683917506335026,2056314197022256097,
%T A088867 3267700501872475297,4544031582110882417,10555434261160919777,
%U A088867 12361929340136667457,23076050051029379057,335875812638910622082
%N A088867 Numbers that can be expressed as the sum of two distinct 4th powers in 
               exactly two distinct ways that have at least one repeated factor.
%H A088867 D. J. Bernstein, <a href="http://cr.yp.to/sortedsums/two4.1000000">List 
               of 516 primitive solutions p^4 + q^4 = r^4 + s^4</a>
%H A088867 Cino Hilliard, <a href="http://www.msnusers.com/BC2LCC/Documents/x4%2By4%2Fx4py4data.txt">
               p,q,r,s and evaluation of the Bernstein data</a>
%H A088867 Cino Hilliard, <a href="http://www.msnusers.com/BC2LCC/Documents/x4%2By4%2Fx4data.txt">
               Evaluation of the Bernstein data only</a>
%F A088867 omega(n)<>bigomega(n) for n = a^4+b^4 = c^4+d^4 for distinct a, b, c, 
               d. n=635318657, 3262811042, .., 680914892583617, .., 962608047985759418078417
%e A088867 The 16th entry in the Bernstein Evaluation = 680914892583617 = 17*17*89*61657*429361 
               = 5 factors. 5 is the 16th entry in the sequence.
%o A088867 (PARI) \ begin a new session and type \r x4data.txt (evaluated Bernstein 
               data) This will allow using %1 as the initial value. omegax4py42(n) 
               = { for (i = 1, n, x = eval( Str("%", i) ); y=omega(x); y1 =bigomega(x); 
               if(y<>y1,print1(x",")) ) }
%Y A088867 Cf. A003824, A088848, A088849.
%Y A088867 Sequence in context: A128769 A086438 A104873 this_sequence A159042 A129935 
               A104835
%Y A088867 Adjacent sequences: A088864 A088865 A088866 this_sequence A088868 A088869 
               A088870
%K A088867 fini,nonn
%O A088867 1,1
%A A088867 Cino Hilliard (hillcino368(AT)gmail.com), Nov 26 2003