A345832 Numbers that are the sum of seven fourth powers in exactly ten ways.

31251, 44547, 45827, 45892, 47667, 47971, 49572, 51092, 53316, 53476, 54531, 54596, 54756, 57411, 58276, 58660, 59781, 59811, 59827, 59861, 59876, 59892, 61076, 64581, 65876, 65891, 66356, 66596, 66676, 67716, 67876, 68131, 68322, 68772, 69171, 69667, 70116

Offset: 1

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

Comments

Differs from A345576 at term 5 because 45907 = 1^4 + 1^4 + 3^4 + 4^4 + 8^4 + 12^4 + 12^4 = 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 + 13^4 = 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 + 13^4 = 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 + 13^4 = 2^4 + 2^4 + 4^4 + 7^4 + 7^4 + 7^4 + 14^4 = 2^4 + 3^4 + 6^4 + 6^4 + 7^4 + 7^4 + 14^4 = 2^4 + 4^4 + 6^4 + 7^4 + 9^4 + 11^4 + 12^4 = 2^4 + 5^4 + 5^4 + 10^4 + 10^4 + 10^4 + 11^4 = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 14^4 = 3^4 + 6^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.

Examples

			44547 is a term because 44547 = 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 11^4 + 13^4 = 1^4 + 2^4 + 2^4 + 6^4 + 7^4 + 7^4 + 14^4 = 1^4 + 2^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 1^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4 = 2^4 + 2^4 + 8^4 + 9^4 + 9^4 + 9^4 + 12^4 = 2^4 + 4^4 + 6^4 + 6^4 + 9^4 + 9^4 + 13^4 = 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 11^4 + 12^4 = 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 12^4 + 12^4 = 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 11^4 + 12^4 = 4^4 + 4^4 + 8^4 + 8^4 + 9^4 + 11^4 + 11^4.
		

Links

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

Crossrefs

Cf. A345576, A345782, A345822, A345831, A345842, A346259.

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 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 == 10])
    for x in range(len(rets)):
        print(rets[x])