A379400 Numbers that can be written in exactly five different ways as a sum of at most nine positive third powers.

133, 145, 152, 153, 159, 160, 161, 163, 182, 190, 192, 196, 197, 198, 200, 201, 209, 218, 220, 223, 225, 226, 233, 234, 235, 236, 237, 238, 246, 248, 249, 255, 258, 265, 268, 269, 274, 277, 279, 292, 300, 302, 304, 305, 310, 311, 312, 329, 331, 340, 356, 364, 365, 429

Offset: 1

Author

Patrick De Geest, Dec 23 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 (A002804).

Examples

			133 is in the sequence since 2^3+5^3 = 1^3+1^3+1^3+1^3+1^3+4^3+4^3 = 1^3+2^3+2^3+2^3+3^3+3^3+3^3+3^3 = 1^3+1^3+1^3+1^3+1^3+1^3+1^3+1^3+5^3 = 1^3+1^3+2^3+2^3+2^3+2^3+2^3+3^3+4^3.
		

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, A379398, A379399.

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==5, v, 1) \\ David A. Corneth, Dec 23 2024