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A345337
Numbers that are the sum of four fifth powers in three or more ways.
4
1479604544, 8429250269, 31738437018, 47347345408, 101802671905, 213625838382, 269736008608, 288202145792, 353946845525, 355891431456, 359543904192, 434029382875, 453675031150, 467943544849, 470899924000, 476304861791, 568433238331, 690221638656, 706199665600
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
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
STATUS
approved