A379396 Numbers that can be written in exactly one way as a sum of at most nine positive third powers.

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 38, 39, 45, 46, 47, 50, 52, 53

Offset: 1

Author

Patrick De Geest, Dec 22 2024

Keywords

• nonn
• more

Comments

The 'nine' is not arbitrary. Waring stated that every natural number can be expressed as a sum of at most nine cubes. (Cf. A002804)

Examples

			7 is in the sequence since there is only 1^3+1^3+1^3+1^3+1^3+1^3+1^3.
53 is in the sequence since there is only 1^3+1^3+2^3+2^3+2^3+3^3;
		

Links

• Eric Weisstein's World of Mathematics, Waring's Problem
• Wikipedia, Waring's Problem
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A002804, A025453, A379397, A379398, A379399, A379400

Programs

PARI

upto(n) = my(v=vector(n), maxb=sqrtnint(n,3)); forvec(x=vector(9,i,[0,maxb]), s=sum(i=1,9,x[i]^3); if(0x==1,v,1) \\ David A. Corneth, Dec 23 2024