A345641 Numbers that are the sum of ten fifth powers in nine or more ways.

1192180, 1226654, 1242437, 1431399, 1431430, 1431641, 1431672, 1431883, 1432453, 1432664, 1434765, 1439174, 1439416, 1441695, 1442718, 1447602, 1448447, 1455346, 1455377, 1464166, 1464377, 1464408, 1474431, 1474462, 1475485, 1491978, 1497619, 1505660, 1531398

Offset: 1

Author

David Consiglio, Jr., Jun 20 2021

Keywords

• nonn

Examples

			1226654 is a term because 1226654 = 1^5 + 1^5 + 4^5 + 5^5 + 7^5 + 8^5 + 9^5 + 13^5 + 13^5 + 13^5 = 1^5 + 1^5 + 5^5 + 7^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 = 1^5 + 2^5 + 2^5 + 4^5 + 6^5 + 10^5 + 12^5 + 12^5 + 12^5 + 13^5 = 1^5 + 2^5 + 2^5 + 4^5 + 7^5 + 10^5 + 11^5 + 11^5 + 12^5 + 14^5 = 1^5 + 3^5 + 3^5 + 3^5 + 7^5 + 10^5 + 10^5 + 10^5 + 13^5 + 14^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 7^5 + 8^5 + 12^5 + 13^5 + 14^5 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 5^5 + 10^5 + 13^5 + 13^5 + 13^5 = 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5 + 8^5 + 9^5 + 16^5 = 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 8^5 + 9^5 + 16^5.
		

Links

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

Crossrefs

Cf. A345602, A345626, A345640, A345642, A346354.

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 >= 9])
    for x in range(len(rets)):
        print(rets[x])