_Cino Hilliard (hillcino368(AT)gmail.com), _, Nov 24 2003

proposed

approved

editing

proposed

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

sequence.

approved

editing

fini,nonn,new

Cino Hilliard (hillcino368(AT)hotmailgmail.com), Nov 24 2003

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

fini,nonn,new

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

D. J. Bernstein, List of 516 primitive solutions p^4 + q^4 = r^4 + s^4 = a(n)<a href="http://cr.yp.to/sortedsums/two4.1000000">List of 516 primitive solutions p^4 + q^4 = r^4 + s^4</a>;

Cino Hilliard, p,q,r,s and evaluation of the Bernstein data .<a href="http://www.msnusers.com/BC2LCC/Documents/x4%2By4%2Fx4py4data.txt">p,q,r,s and evaluation of the Bernstein data</a>;

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

fini,nonn,new

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

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, 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, 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

1,1

D. J. Bernstein, List of 516 primitive solutions p^4 + q^4 = r^4 + s^4 = a(n)<a href="http://cr.yp.to/sortedsums/two4.1000000"></a>;

Cino Hilliard, p,q,r,s and evaluation of the Bernstein data .<a href="http://www.msnusers.com/BC2LCC/Documents/x4%2By4%2Fx4py4data.txt"></a>;

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

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

The 16th entry in the Bernstein Evaluation =

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

sequence.

(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", ") ) }

Cf. A003824.

fini,nonn

Cino Hilliard (hillcino368(AT)hotmail.com), Nov 24 2003

approved