A346345 Numbers that are the sum of nine fifth powers in exactly ten ways.

4157156, 4492410, 4510461, 4915538, 5005474, 5015506, 5179747, 5219655, 5756794, 6323426, 6326519, 6382443, 6423394, 6705284, 6793170, 6861218, 7101038, 7147645, 7147656, 7148679, 7266240, 7280391, 7283268, 7314187, 7413493, 7422352, 7531076, 7651645, 7693425

Offset: 1

Author

David Consiglio, Jr., Jul 13 2021

Keywords

• nonn

Comments

Differs from A345627 at term 5 because 4948274 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 8^5 + 9^5 + 15^5 + 21^5 = 1^5 + 3^5 + 5^5 + 5^5 + 8^5 + 8^5 + 8^5 + 15^5 + 21^5 = 1^5 + 2^5 + 2^5 + 5^5 + 5^5 + 11^5 + 11^5 + 17^5 + 20^5 = 8^5 + 9^5 + 9^5 + 10^5 + 10^5 + 10^5 + 12^5 + 16^5 + 20^5 = 4^5 + 8^5 + 8^5 + 10^5 + 12^5 + 12^5 + 15^5 + 16^5 + 19^5 = 4^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 15^5 + 19^5 = 4^5 + 4^5 + 9^5 + 13^5 + 13^5 + 13^5 + 14^5 + 15^5 + 19^5 = 6^5 + 6^5 + 9^5 + 9^5 + 12^5 + 12^5 + 14^5 + 18^5 + 18^5 = 1^5 + 8^5 + 8^5 + 12^5 + 12^5 + 14^5 + 14^5 + 17^5 + 18^5 = 1^5 + 8^5 + 9^5 + 9^5 + 13^5 + 14^5 + 16^5 + 17^5 + 17^5 = 3^5 + 7^5 + 7^5 + 10^5 + 12^5 + 16^5 + 16^5 + 16^5 + 17^5.

Examples

			4157156 is a term because 4157156 = 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 9^5 + 21^5 = 1^5 + 1^5 + 3^5 + 4^5 + 5^5 + 5^5 + 8^5 + 8^5 + 21^5 = 1^5 + 4^5 + 4^5 + 8^5 + 10^5 + 12^5 + 12^5 + 16^5 + 19^5 = 1^5 + 4^5 + 4^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 19^5 = 5^5 + 5^5 + 5^5 + 5^5 + 7^5 + 9^5 + 15^5 + 17^5 + 18^5 = 3^5 + 3^5 + 5^5 + 6^5 + 9^5 + 10^5 + 16^5 + 16^5 + 18^5 = 1^5 + 1^5 + 5^5 + 5^5 + 13^5 + 13^5 + 15^5 + 15^5 + 18^5 = 2^5 + 3^5 + 4^5 + 4^5 + 10^5 + 14^5 + 16^5 + 16^5 + 17^5 = 11^5 + 11^5 + 12^5 + 12^5 + 12^5 + 12^5 + 13^5 + 16^5 + 17^5 = 2^5 + 2^5 + 2^5 + 5^5 + 12^5 + 15^5 + 16^5 + 16^5 + 16^5.
		

Links

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

Crossrefs

Cf. A345627, A345852, A346335, A346344, A346355.

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, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 10])
    for x in range(len(rets)):
        print(rets[x])