A346357 Numbers that are the sum of six fifth powers in exactly two ways.

4098, 4129, 4340, 5121, 7222, 11873, 20904, 36865, 51447, 51478, 51509, 51689, 51720, 51931, 52470, 52501, 52712, 53493, 54571, 54602, 54813, 55594, 57695, 59222, 59253, 59464, 60245, 62346, 63146, 66997, 67586, 68253, 68284, 68495, 68906, 68937, 69148, 69276

Offset

1,1

Comments

Differs from A345507 at term 231 because 696467 = 1^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 13^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 13^5.

Links

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

Example

4098 is a term because 4098 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 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, 6):
    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. A342686, A345507, A345814, A346279, A346356, A346358.

Sequence in context: A226695 A031562 A345507 * A282548 A253712 A345605

Adjacent sequences: A346354 A346355 A346356 * A346358 A346359 A346360

Keyword

nonn

Author

David Consiglio, Jr., Jul 13 2021

Status

approved