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A345010
Numbers that are the sum of three fifth powers in two or more ways.
5
1375298099, 1419138368, 2370099168, 5839897526, 16681039431, 27326512069, 28461637018, 34090335168, 44009539168, 45412427776, 47166830151, 57788232400, 75843173376, 89516861675, 89636142881, 140201053499, 186876720832, 191701358025, 209797492893, 220333644849
OFFSET
1,1
COMMENTS
No numbers that are the sum of three fifth powers in three ways have been found. As a result, there is no corresponding sequence for the sum of three fifth powers in exactly two ways.
LINKS
David Consiglio, Jr., Table of n, a(n) for n = 1..396
EXAMPLE
1419138368 is a term because 1419138368 = 13^5 + 51^5 + 64^5 = 18^5 + 44^5 + 66^5.
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, 3):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 2])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved