

A345010


Numbers that are the sum of three fifth powers in two or more ways.


4



1375298099, 1419138368, 2370099168, 5839897526, 16681039431, 27326512069, 28461637018, 34090335168, 44009539168, 45412427776, 47166830151, 57788232400, 75843173376, 89516861675, 89636142881, 140201053499, 186876720832, 191701358025, 209797492893, 220333644849
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Cf. A003348, A309762, A344644.
Sequence in context: A346959 A068746 A343078 * A338516 A091443 A114888
Adjacent sequences: A345007 A345008 A345009 * A345011 A345012 A345013


KEYWORD

nonn


AUTHOR

David Consiglio, Jr., Jun 14 2021


STATUS

approved



