A345615 Numbers that are the sum of eight fifth powers in seven or more ways.

4104553, 4915506, 6011150, 6027989, 6323394, 6563733, 6622231, 6776363, 6785394, 7982834, 8181481, 8288806, 8625619, 8658144, 8710484, 8742208, 8773477, 8932244, 8996669, 9252219, 9253706, 9311478, 9773236, 9904983, 9976120, 10036233, 10045233, 10053008

Offset: 1

Author

David Consiglio, Jr., Jun 20 2021

Keywords

• nonn

Examples

			4915506 is a term because 4915506 = 1^5 + 3^5 + 5^5 + 5^5 + 8^5 + 8^5 + 15^5 + 21^5 = 1^5 + 8^5 + 12^5 + 12^5 + 14^5 + 14^5 + 17^5 + 18^5 = 1^5 + 9^5 + 9^5 + 13^5 + 14^5 + 16^5 + 17^5 + 17^5 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 9^5 + 15^5 + 21^5 = 4^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 15^5 + 19^5 = 4^5 + 8^5 + 10^5 + 12^5 + 12^5 + 15^5 + 16^5 + 19^5 = 9^5 + 9^5 + 10^5 + 10^5 + 10^5 + 12^5 + 16^5 + 20^5.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A345582, A345614, A345616, A345624, A345629, A346332.

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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 7])
    for x in range(len(rets)):
        print(rets[x])