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A088848 Number of prime factors, without multiplicity, of numbers that can be expressed as the sum of two distinct 4th powers in exactly two distinct ways.

%I A088848 #5 Oct 01 2013 17:57:45
%S A088848 4,4,4,4,3,4,4,4,6,4,5,6,4,4,7,4,7,4,3,5,6,5,6,5,6,4,5,5,6,5,4,5,4,4,
%T A088848 6,6,6,6,6,6,5,5,6,5,6,6,6,5,7,5,6,4,5,6,6,6,5,6,5,6,4,6,4,7,6,7,5,4,
%U A088848 5,4,5,4,6,6,5,6,5,6,5,7,4,5,6,4,6,4,6,4,5,5,9,5,5,6,6,5,3,4,5,5
%N A088848 Number of prime factors, without multiplicity, of numbers that can be expressed as the sum of two distinct 4th powers in exactly two distinct ways.
%H A088848 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 A088848 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 A088848 Cino Hilliard, <a href="http://www.msnusers.com/BC2LCC/Documents/x4%2By4%2Fx4data.txt">Evaluation of the Bernstein data only</a>
%F A088848 Omega(n) for n = a^4+b^4 = c^4+d^4 for distinct a, b, c, d. n=635318657, 3262811042, .., 960213785093149760746642, 962608047985759418078417
%e A088848 3262811042 = 2*113*2953*4889. Thus 4 is the first entry.
%o A088848 (PARI) \ begin a new session and (back slash)r x4data.txt (evaluated Bernstein data) \ to the gp session. This will allow using %1 as the initial value. omegax4py42(n) = { for (i = 1, n, x = eval( Str("%", i) ); y=omega(x); print(y",") ) }
%Y A088848 Cf. A003824.
%K A088848 fini,nonn
%O A088848 1,1
%A A088848 _Cino Hilliard_, Nov 24 2003