login
A344730
Numbers that are the sum of three fourth powers in exactly seven ways.
6
779888018, 12478208288, 33038379458, 63170929458, 114872872562, 199651332608, 329296962722, 393006728738, 419200136082, 487430011250, 528614071328, 959702600738, 1010734871328, 1369390032738, 1502549262242, 1525400097858, 1653983981762, 1668273965442, 1756039197458, 1793250582818, 1837965960992, 1912768493202
OFFSET
1,1
COMMENTS
Differs from A344729 at term 2 because 5745705602 3^4+ 230^4+ 233^4 = 25^4+ 218^4+ 243^4 = 43^4+ 207^4+ 250^4 = 58^4+ 197^4+ 255^4 = 85^4+ 177^4+ 262^4 = 90^4+ 173^4+ 263^4 = 102^4+ 163^4+ 265^4 = 122^4+ 145^4+ 267^4
LINKS
EXAMPLE
779888018 is a term because 779888018 = 3^4+ 139^4+ 142^4 = 9^4+ 38^4+ 167^4 = 14^4+ 133^4+ 147^4 = 43^4+ 114^4+ 157^4 = 47^4+ 111^4+ 158^4 = 63^4+ 98^4+ 161^4 = 73^4+ 89^4+ 162^4
PROG
(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 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 == 7])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved