login
A343989
Numbers that are the sum of five positive cubes in five or more ways.
8
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
1,1
LINKS
David Consiglio, Jr., Table of n, a(n) for n = 1..20000
EXAMPLE
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.
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, 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])
KEYWORD
nonn
AUTHOR
STATUS
approved