# A332111
## Numbers that are not the sum of eleven (11) positive cubes.

### DATA
```text
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 38, 40, 41, 42, 43, 45, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 61, 62, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 82, 83, 85, 87, 90, 92, 94, 97, 99
```

### PYTHON IMPLEMENTATION
*No Python implementation recorded in the local database yet.*

### PROGRAMS
#### Mathematica
```mathematica
Select[Range[400], (pr = PowersRepresentations[#, 11, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* adapted from _Amiram Eldar_'s code for A332110 *)
```

#### Other Programs
- **(PARI)** :
```pari
A332111=setminus([1..333],A003333_upto(444))
```

### COMMENTS
- The sequence is finite, with last term a(92) = 321.

### EXAMPLES
- The smallest positive numbers not in the sequence are:
- 11 = 11 * 1^3, 18 = 2^3 + 10 * 1^3, 25 = 2 * 2^3 + 9 * 1^3,
- 32 = 3 * 2^3 + 8 * 1^3 and then 37 = 3^3 + 10 * 1^3.
- The last 23 terms of the sequence (not in the data section) are a(70 .. 92) = {101, 104, 106, 108, 111, 113, 118, 120, 125, 127, 132, 134, 139, 146, 153, 160, 171, 190, 197, 209, 216, 223, 321}.

### LINKS
- M. F. Hasler, [Table of n, a(n) for n = 1..92](https://oeis.org/A332111/b332111.txt) (full sequence).
- Brennan Benfield and Oliver Lippard, [Integers that are not the sum of positive powers](https://arxiv.org/abs/2404.08193), arXiv:2404.08193 [math.NT], 2024. See p. 4.

### CROSSREFERENCES
- Complement of [A003334](A003334).
- Cf. [A332107](A332107), [A332108](A332108), [A332109](A332109), [A332110](A332110) (analog for 7, 8, 9 and 10 cubes).
- See also the official entry at <https://oeis.org/A332111>

### METADATA
- **OFFSET** : `1,2`
- **KEYWORDS** : `nonn,fini,full`
- **AUTHOR** : [_M. F. Hasler_](https://oeis.org/wiki/User:M._F._Hasler), Aug 25 2020
- **IDENTIFICATION** : `#12 Apr 18 2024 13:50:44`