A345337 Numbers that are the sum of four fifth powers in three or more ways.

1479604544, 8429250269, 31738437018, 47347345408, 101802671905, 213625838382, 269736008608, 288202145792, 353946845525, 355891431456, 359543904192, 434029382875, 453675031150, 467943544849, 470899924000, 476304861791, 568433238331, 690221638656, 706199665600

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: A165736 A372106 A048051 * A073519 A256891 A320873

Adjacent sequences: A345334 A345335 A345336 * A345338 A345339 A345340

Keyword

nonn

Author

David Consiglio, Jr., Jun 14 2021

Status

approved