This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
6588 is a term because 6588 = 1^3 + 3^3 + 5^3 + 7^3 + 17^3 = 1^3 + 4^3 + 6^3 + 13^3 + 14^3 = 1^3 + 5^3 + 8^3 + 8^3 + 16^3 = 1^3 + 10^3 + 10^3 + 11^3 + 12^3 = 2^3 + 2^3 + 9^3 + 12^3 + 14^3 = 2^3 + 3^3 + 8^3 + 11^3 + 15^3 = 3^3 + 8^3 + 8^3 + 11^3 + 14^3 = 3^3 + 3^3 + 5^3 + 10^3 + 16^3 = 5^3 + 5^3 + 8^3 + 10^3 + 15^3 = 8^3 + 9^3 + 10^3 + 10^3 + 12^3.
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, 5):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 10])
for x in range(len(rets)):
print(rets[x])
84 = 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 8^2 = 1^2 + 1^2 + 1^2 + 3^2 + 6^2 + 6^2 = 1^2 + 1^2 + 1^2 + 4^2 + 4^2 + 7^2 = 1^2 + 1^2 + 2^2 + 2^2 + 5^2 + 7^2 = 1^2 + 1^2 + 4^2 + 4^2 + 5^2 + 5^2 = 1^2 + 2^2 + 2^2 + 5^2 + 5^2 + 5^2 = 1^2 + 2^2 + 3^2 + 3^2 + 5^2 + 6^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 8^2 = 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 7^2 = 2^2 + 4^2 + 4^2 + 4^2 + 4^2 + 4^2 = 3^2 + 3^2 + 3^2 + 4^2 + 4^2 + 5^2 so 84 is a term.
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 10])
for x in range(len(rets)):
print(rets[x])