A343989 Numbers that are the sum of five positive cubes in five or more ways.

1765, 1980, 2043, 2104, 2195, 2250, 2430, 2449, 2486, 2491, 2493, 2547, 2584, 2592, 2738, 2745, 2764, 2817, 2888, 2915, 2953, 2969, 2979, 3095, 3096, 3133, 3142, 3186, 3188, 3214, 3240, 3249, 3275, 3277, 3310, 3312, 3366, 3403, 3422, 3459, 3464, 3466, 3483, 3492, 3520, 3529, 3583, 3608, 3627, 3653, 3664, 3671

Offset: 1

Author

David Consiglio, Jr., May 06 2021

Keywords

• nonn

Examples

			2043 = 1^3 + 4^3 + 5^3 +  5^3 + 12^3
     = 2^3 + 2^3 + 3^3 + 10^3 + 10^3
     = 2^3 + 3^3 + 4^3 +  6^3 + 12^3
     = 4^3 + 5^3 + 5^3 +  9^3 + 10^3
     = 4^3 + 6^3 + 6^3 +  6^3 + 11^3
so 2043 is a term.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A343987, A343988, A344034, A344358, A344798, A345174, A345514.

Programs

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(1,50)]
for pos in cwr(power_terms,5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 5])
for x in range(len(rets)):
    print(rets[x])