A345722 Numbers that are the sum of six fifth powers in eight or more ways.

2295937600, 4335900525, 6251954544, 8986552608, 9085584992, 13413708308, 14539246326, 15277569450, 15728636000, 16770321920, 16873011232, 16933805856, 17572402769, 17713454592, 17960776999, 18190647200, 19621666592, 20570070125, 20827689300

Offset: 1

Author

David Consiglio, Jr., Jun 24 2021

Keywords

• nonn

Examples

			4335900525 is a term because 4335900525 = 2^5 + 24^5 + 34^5 + 56^5 + 61^5 + 78^5 = 3^5 + 21^5 + 37^5 + 54^5 + 62^5 + 78^5 = 3^5 + 21^5 + 39^5 + 49^5 + 66^5 + 77^5 = 3^5 + 26^5 + 32^5 + 49^5 + 72^5 + 73^5 = 8^5 + 16^5 + 42^5 + 49^5 + 61^5 + 79^5 = 9^5 + 13^5 + 43^5 + 47^5 + 66^5 + 77^5 = 19^5 + 20^5 + 30^5 + 45^5 + 61^5 + 80^5 = 21^5 + 24^5 + 28^5 + 37^5 + 67^5 + 78^5.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..389

Crossrefs

Cf. A345565, A345630, A345721, A345723, A346363.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 8])
    for x in range(len(rets)):
        print(rets[x])