A345828 Numbers that are the sum of seven fourth powers in exactly six ways.

10787, 15396, 15411, 15586, 15651, 16611, 16626, 16676, 16866, 17956, 18867, 19156, 19236, 19251, 19411, 19426, 19666, 20035, 20771, 21012, 21187, 21397, 21412, 21442, 21492, 21572, 21621, 21811, 21891, 22116, 22132, 22292, 22307, 22372, 22595, 22660, 22962

Offset

1,1

Comments

Differs from A345572 at term 9 because 16691 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4 = 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4 = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4 = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.

Links

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

Example

15396 is a term because 15396 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 11^4 = 1^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 9^4 + 9^4.

Prog

(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 == 6])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345572, A345778, A345818, A345827, A345829, A345838, A346283.

Sequence in context: A034231 A229275 A345572 * A151934 A151935 A010089

Adjacent sequences: A345825 A345826 A345827 * A345829 A345830 A345831

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved