A345819 Numbers that are the sum of six fourth powers in exactly seven ways.

21251, 43875, 48276, 49796, 53315, 58500, 59795, 59811, 67875, 68306, 69155, 69779, 71955, 72051, 72131, 73970, 74420, 74851, 77010, 80291, 80515, 81875, 82275, 84515, 86436, 86451, 86531, 87075, 88355, 88660, 88675, 90355, 91475, 93410, 93650, 94690, 95155

Offset

1,1

Comments

Differs from A345564 at term 6 because 58035 = 1^4 + 1^4 + 9^4 + 10^4 + 12^4 + 12^4 = 1^4 + 4^4 + 5^4 + 8^4 + 11^4 + 14^4 = 1^4 + 5^4 + 6^4 + 11^4 + 12^4 + 12^4 = 2^4 + 2^4 + 4^4 + 5^4 + 13^4 + 13^4 = 2^4 + 6^4 + 6^4 + 7^4 + 7^4 + 15^4 = 2^4 + 8^4 + 10^4 + 11^4 + 11^4 + 11^4 = 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 15^4 = 4^4 + 5^4 + 6^4 + 9^4 + 12^4 + 13^4.

Links

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

Example

43875 is a term because 43875 = 1^4 + 2^4 + 9^4 + 9^4 + 10^4 + 12^4 = 2^4 + 2^4 + 2^4 + 5^4 + 11^4 + 13^4 = 2^4 + 2^4 + 5^4 + 7^4 + 7^4 + 14^4 = 2^4 + 5^4 + 6^4 + 9^4 + 11^4 + 12^4 = 3^4 + 7^4 + 8^4 + 9^4 + 10^4 + 12^4 = 4^4 + 4^4 + 7^4 + 7^4 + 10^4 + 13^4 = 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.

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

Crossrefs

Cf. A344943, A345564, A345769, A345818, A345820, A345829, A346362.

Sequence in context: A217265 A345563 A345564 * A345830 A236644 A178282

Adjacent sequences: A345816 A345817 A345818 * A345820 A345821 A345822

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved