A379398 Numbers that can be written in exactly three different ways as a sum of at most nine positive third powers.

35, 56, 64, 65, 67, 68, 70, 75, 81, 82, 83, 84, 86, 89, 92, 93, 94, 96, 97, 98, 99, 100, 105, 107, 108, 110, 112, 113, 118, 119, 120, 121, 124, 125, 127, 130, 141, 142, 143, 148, 149, 150, 151, 167, 169, 174, 175, 176, 177, 178, 183, 186, 188, 202, 204, 212, 213, 214, 240, 247, 303

Offset: 1

Author

Patrick De Geest, Dec 22 2024

Keywords

• nonn

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

			67 is in the sequence since 1^3+1^3+1^3+4^3 = 2^3+2^3+2^3+2^3+2^3+3^3 = 1^3+1^3+1^3+1^3+1^3+2^3+3^3+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, A379396, A379397, 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==3,v,1)) \\ David A. Corneth, Dec 23 2024