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A345830 Numbers that are the sum of seven fourth powers in exactly eight ways. 8
21252, 21507, 21636, 21876, 25347, 30372, 31412, 31652, 32116, 32356, 33811, 33907, 35637, 35652, 35892, 36261, 37827, 38052, 38596, 38676, 39267, 39347, 39971, 39972, 40212, 40452, 41506, 41731, 41987, 42147, 42227, 42357, 42532, 42771, 42852, 43027, 43282 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A345574 at term 1 because 19491 = 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 8^4 + 10^4  = 1^4 + 2^4 + 4^4 + 4^4 + 7^4 + 9^4 + 10^4  = 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 8^4 + 9^4  = 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 9^4 + 10^4  = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 8^4 + 11^4  = 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 7^4 + 11^4  = 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 8^4 + 10^4  = 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 11^4  = 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 8^4.

LINKS

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

EXAMPLE

21252 is a term because 21252 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 12^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4 = 1^4 + 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4 = 1^4 + 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 = 1^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4 = 3^4 + 4^4 + 6^4 + 7^4 + 8^4 + 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 == 8])

    for x in range(len(rets)):

        print(rets[x])

CROSSREFS

Cf. A345574, A345780, A345820, A345829, A345831, A345840, A346285.

Sequence in context: A345563 A345564 A345819 * A236644 A178282 A234408

Adjacent sequences:  A345827 A345828 A345829 * A345831 A345832 A345833

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 26 2021

STATUS

approved

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Last modified August 12 20:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)