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

1,3

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..33.

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

Wikipedia, Waring's Problem

Index entries for sequences related to sums of cubes

Example

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;

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

Crossrefs

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

Sequence in context: A000433 A031492 A350076 * A393981 A389215 A035060

Adjacent sequences: A379393 A379394 A379395 * A379397 A379398 A379399

Keyword

nonn,more

Author

Patrick De Geest, Dec 22 2024

Status

approved