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A345781 Numbers that are the sum of seven cubes in exactly nine ways. 7
1496, 1648, 1720, 1737, 1772, 1781, 1802, 1835, 1844, 1882, 1891, 1898, 1900, 1907, 1912, 1919, 1945, 1952, 1954, 1961, 1996, 2000, 2012, 2026, 2071, 2080, 2098, 2107, 2110, 2115, 2116, 2132, 2134, 2136, 2139, 2150, 2152, 2168, 2178, 2185, 2187, 2195, 2205 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A345527 at term 3 because 1704 = 1^3 + 1^3 + 1^3 + 3^3 + 6^3 + 9^3 + 9^3  = 1^3 + 1^3 + 1^3 + 4^3 + 5^3 + 8^3 + 10^3  = 1^3 + 1^3 + 2^3 + 2^3 + 7^3 + 7^3 + 10^3  = 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 6^3 + 11^3  = 1^3 + 2^3 + 4^3 + 6^3 + 7^3 + 7^3 + 9^3  = 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 6^3 + 11^3  = 2^3 + 2^3 + 3^3 + 5^3 + 8^3 + 8^3 + 8^3  = 3^3 + 3^3 + 3^3 + 4^3 + 6^3 + 7^3 + 10^3  = 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 9^3 + 9^3  = 3^3 + 6^3 + 6^3 + 6^3 + 7^3 + 7^3 + 7^3.

Likely finite.

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..338

EXAMPLE

1648 is a term because 1648 = 1^3 + 1^3 + 1^3 + 2^3 + 4^3 + 7^3 + 9^3 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 10^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 10^3 = 1^3 + 1^3 + 3^3 + 4^3 + 5^3 + 7^3 + 8^3 = 1^3 + 2^3 + 2^3 + 5^3 + 6^3 + 6^3 + 8^3 = 1^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 + 9^3 = 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 6^3 + 9^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 8^3 + 8^3 = 3^3 + 3^3 + 3^3 + 5^3 + 5^3 + 7^3 + 7^3.

PROG

(Python)

from itertools import combinations_with_replacement as cwr

from collections import defaultdict

keep = defaultdict(lambda: 0)

power_terms = [x**3 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 == 9])

    for x in range(len(rets)):

        print(rets[x])

CROSSREFS

Cf. A345527, A345771, A345780, A345782, A345791, A345831.

Sequence in context: A062912 A328975 A345527 * A328974 A236732 A184078

Adjacent sequences:  A345778 A345779 A345780 * A345782 A345783 A345784

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 26 2021

STATUS

approved

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Last modified October 5 21:20 EDT 2022. Contains 357261 sequences. (Running on oeis4.)