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A345819 Numbers that are the sum of six fourth powers in exactly seven ways. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 20:35 EDT 2021. Contains 348233 sequences. (Running on oeis4.)