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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

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Last modified December 8 11:53 EST 2021. Contains 349596 sequences. (Running on oeis4.)