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A343972

Numbers that are the sum of four positive cubes in exactly four ways.

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

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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)