A345010 Numbers that are the sum of three fifth powers in two or more ways.

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

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