A346352 Numbers that are the sum of ten fifth powers in exactly seven ways.

555098, 674040, 683166, 707315, 763631, 777852, 778844, 780945, 783224, 893654, 896500, 897668, 920887, 926616, 927819, 928802, 936850, 937631, 945017, 952897, 953077, 953350, 955178, 963131, 975133, 979482, 984133, 985664, 987257, 991908, 993575, 993606

Offset: 1

Author

David Consiglio, Jr., Jul 13 2021

Keywords

• nonn

Comments

Differs from A345639 at term 19 because 944383 = 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 8^5 + 8^5 + 8^5 + 9^5 + 15^5 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 + 10^5 + 12^5 + 14^5 = 2^5 + 4^5 + 5^5 + 5^5 + 7^5 + 7^5 + 7^5 + 10^5 + 12^5 + 14^5 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 + 11^5 + 11^5 + 14^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 11^5 + 11^5 + 14^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 = 1^5 + 3^5 + 4^5 + 6^5 + 7^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 10^5 + 11^5 + 11^5 + 12^5 + 12^5.

Examples

			555098 is a term because 555098 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 7^5 + 14^5 = 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 7^5 + 8^5 + 10^5 + 13^5 = 1^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 7^5 + 10^5 + 13^5 = 1^5 + 2^5 + 5^5 + 7^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 13^5 = 4^5 + 4^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 11^5 + 12^5 = 3^5 + 3^5 + 4^5 + 4^5 + 6^5 + 7^5 + 9^5 + 9^5 + 11^5 + 12^5 = 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 + 11^5.
		

Links

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

Crossrefs

Cf. A345639, A345859, A346342, A346351, A346353.

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 == 7])
    for x in range(len(rets)):
        print(rets[x])