A345815 Numbers that are the sum of six fourth powers in exactly three ways.

2676, 2851, 2916, 4131, 4226, 4241, 4306, 4371, 4481, 4850, 5346, 5411, 5521, 5586, 5651, 6561, 6611, 6756, 6771, 6801, 6821, 6836, 6851, 6931, 7106, 7235, 7475, 7491, 7666, 7841, 7906, 7971, 8146, 8211, 8321, 8386, 8451, 8531, 8706, 9011, 9156, 9171, 9186

Offset

1,1

Comments

Differs from A345560 at term 18 because 6626 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.

Links

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

Example

2851 is a term because 2851 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 3])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A048931, A344244, A345560, A345814, A345816, A345825, A346358.

Sequence in context: A123075 A112138 A345560 * A166513 A345569 A345825

Adjacent sequences: A345812 A345813 A345814 * A345816 A345817 A345818

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved