A345084 Numbers that are the sum of three third powers in exactly six ways.

1296378, 1371735, 1409400, 1614185, 1824040, 1885248, 2101464, 2302028, 2305395, 2542968, 2851848, 2889216, 2974392, 2988441, 3185792, 3380833, 3681280, 3689496, 3706984, 3775680, 3906657, 4109832, 4123008, 4142683, 4422592, 4842872, 4952312, 5005125, 5023656

Offset: 1

Author

David Consiglio, Jr., Jun 07 2021

Keywords

• nonn

Comments

Differs from A345083 at term 7 because 2016496 = 5^3 + 71^3 + 117^3 = 9^3 + 65^3 + 119^3 = 18^3 + 20^3 + 125^3 = 46^3 + 96^3 + 99^3 = 53^3 + 59^3 + 117^3 = 65^3 + 89^3 + 99^3 = 82^3 + 84^3 + 93^3.

Examples

			1296378 is a term because 1296378 = 3^3 + 75^3 + 94^3  = 8^3 + 32^3 + 107^3  = 20^3 + 76^3 + 93^3  = 30^3 + 58^3 + 101^3  = 32^3 + 80^3 + 89^3  = 59^3 + 74^3 + 86^3.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A025326, A343970, A344648, A345083, A345085, 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, 1000)]
for pos in cwr(power_terms, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 6])
for x in range(len(rets)):
    print(rets[x])