A345783 Numbers that are the sum of eight cubes in exactly one way.

8, 15, 22, 29, 34, 36, 41, 43, 48, 50, 55, 57, 60, 62, 64, 67, 69, 71, 74, 76, 78, 81, 83, 85, 86, 88, 92, 93, 95, 97, 99, 100, 102, 104, 106, 107, 111, 112, 113, 114, 118, 119, 120, 121, 123, 125, 126, 130, 133, 134, 137, 138, 140, 141, 144, 145, 146, 148

Offset

1,1

Comments

Differs from A003331 at term 49 because 132 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.

Likely finite.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..209

Example

15 is a term because 15 = 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, 8):
    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. A003331, A345773, A345784, A345793, A345833.

Sequence in context: A003786 A008686 A003331 * A016993 A079043 A291747

Adjacent sequences: A345780 A345781 A345782 * A345784 A345785 A345786

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved