A346285 Numbers that are the sum of seven fifth powers in exactly eight ways.

36620574, 80552143, 81401376, 82078424, 92347417, 93653176, 94486699, 94626949, 98873875, 105674625, 121050874, 125959393, 129228307, 144209018, 145340799, 147245218, 147898763, 151727082, 151923168, 152361276, 152664876, 153877208, 155107349, 155270357

Offset: 1

Author

David Consiglio, Jr., Jul 12 2021

Keywords

• nonn

Comments

Differs from A345630 at term 11 because 110276376 = 1^5 + 3^5 + 5^5 + 7^5 + 17^5 + 23^5 + 40^5 = 5^5 + 10^5 + 16^5 + 16^5 + 19^5 + 20^5 + 40^5 = 1^5 + 8^5 + 14^5 + 16^5 + 21^5 + 27^5 + 39^5 = 7^5 + 8^5 + 11^5 + 14^5 + 16^5 + 33^5 + 37^5 = 4^5 + 7^5 + 8^5 + 13^5 + 26^5 + 31^5 + 37^5 = 1^5 + 5^5 + 6^5 + 20^5 + 28^5 + 29^5 + 37^5 = 3^5 + 3^5 + 7^5 + 18^5 + 27^5 + 32^5 + 36^5 = 6^5 + 12^5 + 18^5 + 25^5 + 30^5 + 31^5 + 34^5 = 6^5 + 10^5 + 20^5 + 27^5 + 27^5 + 33^5 + 33^5.

Examples

			36620574 is a term because 36620574 = 4^5 + 9^5 + 14^5 + 17^5 + 18^5 + 21^5 + 31^5 = 1^5 + 12^5 + 13^5 + 14^5 + 20^5 + 24^5 + 30^5 = 8^5 + 9^5 + 12^5 + 13^5 + 16^5 + 27^5 + 29^5 = 5^5 + 7^5 + 7^5 + 20^5 + 23^5 + 23^5 + 29^5 = 17^5 + 18^5 + 20^5 + 20^5 + 20^5 + 20^5 + 29^5 = 2^5 + 7^5 + 14^5 + 14^5 + 23^5 + 26^5 + 28^5 = 4^5 + 8^5 + 8^5 + 17^5 + 23^5 + 27^5 + 27^5 = 2^5 + 3^5 + 14^5 + 18^5 + 24^5 + 26^5 + 27^5.
		

Links

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

Crossrefs

Cf. A345630, A345830, A346284, A346286, A346333, A346363.

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