A345624 Numbers that are the sum of nine fifth powers in seven or more ways.

1431398, 1431429, 1431640, 1439173, 1447570, 1504636, 1531397, 1597929, 1671167, 1696159, 1697686, 1697928, 1778835, 1936454, 1952415, 1969221, 1975049, 2017344, 2092122, 2182161, 2198967, 2208680, 2247917, 2280818, 2283911, 2289343, 2314335, 2329845, 2340319

Offset: 1

Author

David Consiglio, Jr., Jun 20 2021

Keywords

• nonn

Examples

			1431429 is a term because 1431429 = 1^5 + 2^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 10^5 + 14^5 + 15^5 = 2^5 + 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 2^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 2^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5.
		

Links

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

Crossrefs

Cf. A345591, A345615, A345623, A345625, A345639, A346342.

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