A345793 Numbers that are the sum of nine cubes in exactly one way.

9, 16, 23, 30, 35, 37, 42, 44, 49, 51, 56, 58, 61, 63, 65, 68, 70, 75, 77, 79, 82, 84, 86, 87, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 107, 108, 110, 112, 113, 114, 115, 119, 120, 121, 122, 124, 126, 127, 128, 129, 131, 134, 135, 138, 139, 141, 142, 145

Offset

1,1

Comments

Differs from A003332 at term 18 because 72 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^2 + 1^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3.

Likely finite.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..176

Example

16 is a term because 16 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3.

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 1])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A003332, A345783, A345794, A345803, A345843.

Sequence in context: A199859 A046463 A003332 * A091571 A225231 A151973

Adjacent sequences: A345790 A345791 A345792 * A345794 A345795 A345796

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved