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

1,1

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)

Links

Table of n, a(n) for n=1..61.

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

Wikipedia, Waring's Problem

Index entries for sequences related to sums of cubes

Example

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.

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); Vec(select(x->x==3, v, 1)) \\ David A. Corneth, Dec 23 2024

Crossrefs

Cf. A002804, A025453, A379396, A379397, A379399, A379400

Sequence in context: A176255 A355814 A090877 * A048033 A254366 A242291

Adjacent sequences: A379395 A379396 A379397 * A379399 A379400 A379401

Keyword

nonn

Author

Patrick De Geest, Dec 22 2024

Status

approved