A379399 Numbers that can be written in exactly four different ways as a sum of at most nine positive third powers.

72, 91, 126, 128, 129, 131, 132, 134, 135, 136, 137, 138, 139, 140, 144, 146, 147, 154, 155, 156, 157, 158, 162, 164, 165, 166, 168, 170, 171, 172, 173, 179, 180, 181, 184, 185, 187, 191, 193, 194, 195, 199, 203, 205, 206, 207, 210, 211, 215, 221, 228, 229, 230, 231, 232, 241, 242, 266, 267, 293, 295, 319, 330, 338, 366, 455

Offset

1,1

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).

Conjecture: this sequence is finite and a(66) = 455 is the last term. Verified up to 10^8. - Charles R Greathouse IV, Dec 28 2024

Links

Table of n, a(n) for n=1..66.

Eric Weisstein's World of Mathematics, Waring's Problem.

Wikipedia, Waring's Problem.

Index entries for sequences related to sums of cubes.

Example

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

Prog

(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(0<s && s<=n, v[s]++); , 1); select(x->x==4, v, 1) \\ David A. Corneth, Dec 23 2024

Crossrefs

Cf. A002804, A025453, A379396, A379397, A379398, A379400.

Sequence in context: A039364 A043967 A248970 * A066943 A206264 A063922

Adjacent sequences: A379396 A379397 A379398 * A379400 A379401 A379402

Keyword

nonn

Author

Patrick De Geest, Dec 23 2024

Status

approved