A126658 Prime numbers that are the sum of three distinct positive eighth powers.

72353, 1745153, 7444673, 44726593, 49202147, 61503553, 100006817, 100072097, 101686177, 107444417, 143046977, 214756067, 257412163, 430372577, 431661313, 435812033, 447149537, 452523713, 489805633, 530372321, 744340577, 834187553

Offset: 1

Author

Tomas Xordan, Feb 09 2007

Keywords

• nonn

Comments

These are also the sum of three squares and the sum of three fourth powers: 7444673 = 16^2 + 1296^2 + 2401^2 = 4^4 + 36^4 + 49^4 = 256 + 1679616 + 5764801.

Examples

			72353 = 2^8 + 3^8 + 4^8 = 256 + 6561 + 65536.
7444673 = 2^8 + 6^8 + 7^8 = 256 + 1679616 + 5764801.
49202147 = 5^8 + 7^8 + 9^8 = 390625 + 5764801 + 43046721.
		

Crossrefs

Cf. A125516, A126657.

Programs

PARI

{m=14;p=m^8;v=vector(m,x,x^8);w=[];for(i=1,m-2,for(j=i+1,m-1, for(k=j+1,m,if((n=v[i]+v[j]+v[k])
				

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 11 2007