OFFSET
1,1
COMMENTS
No numbers that are the sum of four fifth powers in four ways have been found. As a result, there is no corresponding sequence for the sum of four fifth powers in exactly three ways.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..500
EXAMPLE
8429250269 is a term because 8429250269 = 4^5 + 41^5 + 73^5 + 91^5 = 13^5 + 28^5 + 82^5 + 86^5 = 21^5 + 27^5 + 68^5 + 93^5.
PROG
(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 3])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
David Consiglio, Jr., Jun 14 2021
STATUS
approved