%I #8 Oct 01 2013 17:57:45

%S 4,4,4,4,3,4,4,4,6,4,5,6,4,4,7,5,7,4,3,5,6,5,6,5,6,4,5,5,6,5,4,5,4,4,

%T 6,6,6,6,6,6,5,5,6,5,6,6,7,5,7,5,6,4,5,6,6,6,5,6,5,6,4,6,4,7,6,7,5,4,

%U 5,4,5,4,6,6,5,6,6,6,5,7,4,5,6,4,6,5,6,4,5,8,9,5,5,6,6,5,3,5,8,5,7,5,7,6,4

%N Number of prime factors, with multiplicity, of numbers that can be expressed as the sum of two distinct 4th powers in exactly two distinct ways.

%H 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 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 Cino Hilliard, <a href="http://www.msnusers.com/BC2LCC/Documents/x4%2By4%2Fx4data.txt">Evaluation of the Bernstein data only</a>

%F Bigomega(n) for n = a^4+b^4 = c^4+d^4 for distinct a, b, c, d. n=635318657, 3262811042, .., 680914892583617, .., 962608047985759418078417

%e The 16th entry in the Bernstein Evaluation =

%e 680914892583617 = 17*17*89*61657*429361 = 5 factors. 5 is the 16th entry in the sequence.

%o (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. bigomegax4py42(n) = { for (i = 1, n, x = eval( Str("%", i) ); y=bigomega(x); print(y",") ) }

%Y Cf. A003824.

%K fini,nonn

%O 1,1

%A _Cino Hilliard_, Nov 24 2003