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.

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, 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, 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

Offset: 1

Author

Cino Hilliard, Nov 24 2003

Keywords

• fini
• nonn

Examples

			3262811042 = 2*113*2953*4889. Thus 4 is the first entry.
		

Links

• D. J. Bernstein, List of 516 primitive solutions p^4 + q^4 = r^4 + s^4
• Cino Hilliard, p,q,r,s and evaluation of the Bernstein data
• Cino Hilliard, Evaluation of the Bernstein data only

Crossrefs

Cf. A003824.

Programs

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",") ) }

Formula

Omega(n) for n = a^4+b^4 = c^4+d^4 for distinct a, b, c, d. n=635318657, 3262811042, .., 960213785093149760746642, 962608047985759418078417