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

Author

David Consiglio, Jr., Jun 14 2021

Keywords

• nonn

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.

Examples

			1419138368 is a term because 1419138368 = 13^5 + 51^5 + 64^5  = 18^5 + 44^5 + 66^5.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..396

Crossrefs

Cf. A003348, A309762, A344644.

Programs

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])