A345634 Numbers that are the sum of ten fifth powers in two or more ways.

4102, 4133, 4164, 4195, 4226, 4257, 4344, 4375, 4406, 4437, 4468, 4586, 4617, 4648, 4679, 4828, 4859, 4890, 5070, 5101, 5125, 5156, 5187, 5218, 5249, 5312, 5367, 5398, 5429, 5460, 5609, 5640, 5671, 5851, 5882, 6093, 6148, 6179, 6210, 6241, 6390, 6421, 6452

Offset: 1

Author

David Consiglio, Jr., Jun 20 2021

Keywords

• nonn

Examples

			4133 is a term because 4133 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003355, A345595, A345619, A345635, A346347.

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, 10):
    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])