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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 (list; graph; refs; listen; history; text; internal format)
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

Sean A. Irvine, Table of n, a(n) for n = 1..500

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

Cf. A342687, A344241, A344644.

Sequence in context: A129249 A165736 A048051 * A073519 A256891 A320873

Adjacent sequences:  A345334 A345335 A345336 * A345338 A345339 A345340

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 14 2021

STATUS

approved

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Last modified December 6 04:52 EST 2021. Contains 349562 sequences. (Running on oeis4.)