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A346327 Numbers that are the sum of eight fifth powers in exactly two ways. 7
4100, 4131, 4162, 4193, 4342, 4373, 4404, 4584, 4615, 4826, 5123, 5154, 5185, 5365, 5396, 5607, 6146, 6177, 6388, 7169, 7224, 7255, 7286, 7466, 7497, 7708, 8247, 8278, 8489, 9270, 10348, 10379, 10590, 11371, 11875, 11906, 11937, 12117, 12148, 12359, 12898 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A345610 at term 128 because 52417 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5 + 8^5 = 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5.

LINKS

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

EXAMPLE

4100 is a term because 4100 = 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.

PROG

(Python)

from itertools import combinations_with_replacement as cwr

from collections import defaultdict

keep = defaultdict(lambda: 0)

power_terms = [x**5 for x in range(1, 1000)]

for pos in cwr(power_terms, 8):

    tot = sum(pos)

    keep[tot] += 1

    rets = sorted([k for k, v in keep.items() if v == 2])

    for x in range(len(rets)):

        print(rets[x])

CROSSREFS

Cf. A345610, A345834, A346279, A346326, A346328, A346337.

Sequence in context: A023354 A226694 A345610 * A043476 A168191 A045036

Adjacent sequences:  A346324 A346325 A346326 * A346328 A346329 A346330

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jul 13 2021

STATUS

approved

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Last modified August 10 11:03 EDT 2022. Contains 356039 sequences. (Running on oeis4.)