A343986 Numbers that are the sum of four positive cubes in exactly five ways.

5105, 5131, 5616, 5859, 6435, 7777, 9315, 9737, 9793, 10017, 10250, 10458, 10936, 10962, 11000, 11060, 11088, 11592, 11664, 11781, 12168, 12229, 12285, 12320, 12385, 12392, 12707, 13384, 13734, 13832, 13904, 14183, 14239, 14833, 15176, 15596, 15624, 15752, 15759, 15778, 16093, 16289, 16354, 16480, 16569

Offset: 1

Author

David Consiglio, Jr., May 06 2021

Keywords

• nonn

Comments

Differs from A343987 at term 6 because 6883 = 2^3 + 2^3 + 2^3 + 19^3 = 2^3 + 5^3 + 15^3 + 15^3 = 3^3 + 8^3 + 8^3 + 18^3 = 4^3 + 11^3 + 14^3 + 14^3 = 5^3 + 11^3 + 11^3 + 16^3 = 8^3 + 9^3 + 9^3 + 17^3.

Examples

			5616 is a term because 5616 = 1^3 + 8^3 + 12^3 + 15^3 = 2^3 + 8^3 + 10^3 + 16^3 = 4^3 + 4^3 + 14^3 + 14^3 = 4^3 + 5^3 + 11^3 + 16^3 = 8^3 + 9^3 + 10^3 + 15^3.
		

Links

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

Crossrefs

Cf. A025361, A343970, A343972, A343987, A343988, A344357, A345149.

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,4):
    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])