A345120 Numbers that are the sum of three third powers in exactly nine ways.

14926248, 16819704, 20168784, 44946000, 45580536, 54042624, 59768064, 62099136, 66203136, 67956624, 69393024, 78008832, 78716448, 79539832, 80621568, 80996544, 89354448, 90757584, 99616392, 100088568, 101352168, 101943360, 112216896, 112720896, 114306984

Offset: 1

Author

David Consiglio, Jr., Jun 08 2021

Keywords

• nonn

Comments

Differs from A345119 at term 4 because 34012224 = 35^3 + 215^3 + 287^3 = 38^3 + 152^3 + 311^3 = 40^3 + 113^3 + 318^3 = 44^3 + 245^3 + 266^3 = 71^3 + 113^3 + 317^3 = 99^3 + 191^3 + 295^3 = 101^3 + 226^3 + 276^3 = 117^3 + 185^3 + 295^3 = 161^3 + 215^3 + 269^3 = 172^3 + 213^3 + 266^3.

Examples

			14926248 is a term because 14926248 = 2^3 + 33^3 + 245^3  = 11^3 + 185^3 + 203^3  = 14^3 + 32^3 + 245^3  = 50^3 + 113^3 + 236^3  = 71^3 + 89^3 + 239^3  = 74^3 + 189^3 + 196^3  = 89^3 + 185^3 + 197^3  = 98^3 + 148^3 + 219^3  = 105^3 + 149^3 + 217^3.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..6359

Crossrefs

Cf. A025329, A344751, A345088, A345119, A345122, A345154.

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 == 9])
for x in range(len(rets)):
    print(rets[x])