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A343972
Numbers that are the sum of four positive cubes in exactly four ways.
7
1979, 2737, 3663, 4384, 4445, 4474, 4949, 5257, 5320, 5473, 5499, 5553, 5733, 5768, 5833, 5852, 6064, 6104, 6328, 6372, 6587, 6643, 6832, 6912, 6974, 7000, 7030, 7120, 7217, 7371, 7560, 7686, 7840, 8099, 8108, 8281, 8316, 8344, 8379, 8414, 8505, 8568, 8927, 9016, 9018, 9044, 9072, 9100, 9289, 9548, 9648, 9800
OFFSET
1,1
COMMENTS
This sequence varies from A343971 at term 8 because 5105 = 1^3 + 1^3 + 12^3 + 15^3 = 1^3 + 2^3 + 10^3 + 16^3 = 1^3 + 9^3 + 10^3 + 15^3 = 4^3 + 4^3 + 4^3 + 17^3 = 4^3 + 6^3 + 9^3 + 16^3.
LINKS
David Consiglio, Jr., Table of n, a(n) for n = 1..20000
EXAMPLE
3663 is a term because 3663 = 1^3 + 10^3 + 11^3 + 11^3 = 2^3 + 4^3 + 6^3 + 15^3 = 2^3 + 9^3 + 9^3 + 13^3 = 4^3 + 7^3 + 8^3 + 14^3.
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, 50)]
for pos in cwr(power_terms, 4):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 4])
for x in range(len(rets)):
print(rets[x])
KEYWORD
nonn
AUTHOR
STATUS
approved