A126704 Prime numbers that are the sum of three distinct positive sixth powers.

4889, 50753, 51481, 66377, 262937, 308801, 797681, 840241, 1000793, 1046657, 1772291, 2303003, 2986777, 3032641, 3107729, 3365777, 4757609, 4804201, 5135609, 7530329, 7534361, 8061041, 8065073, 10516249, 12394721, 14638753

Offset: 1

Author

Tomas Xordan, Feb 11 2007

Keywords

• nonn

Examples

			4889 = 2^6 + 3^6 + 4^6 = 64 + 729 + 4096.
66377 = 4^6 + 5^6 + 6^6 = 4096 + 15625 + 46656.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125516, A126657, A126658.

Programs

Maple

N:= 10^10; # to find all terms <= N
A := {}:
for a from 1 to iroot(N,6) do
  for b from 1 to a-1 while a^6 + b^6 < N do
    for c from (a+b) mod 2 + 1 to b-1 by 2 do
      r:= a^6 + b^6 + c^6;
      if r > N then break fi;
      if isprime(r) then A:= A union {r} fi;
od od od:
sort(convert(A,list)); # Robert Israel, Dec 15 2015

Mathematica

Union[Select[Total/@Subsets[Range[20]^6,{3}],PrimeQ]] (* Harvey P. Dale, Apr 20 2013 *)

PARI

{m=16; p=m^6; w=[]; for(i=1,m-2,for(j=i+1, m-1, for(k=j+1, m, if((n=i^6+j^6+k^6)Klaus Brockhaus, Feb 16 2007 */

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 16 2007