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A346348 Numbers that are the sum of ten fifth powers in exactly three ways. 6

%I #6 Jul 31 2021 18:54:02

%S 8194,21940,52419,52450,52481,52661,52692,52903,53442,53473,53684,

%T 54465,54520,54551,54582,54762,54793,55004,55691,55722,55933,56714,

%U 57644,57675,57886,58815,60194,60225,60436,60768,61217,62295,62326,62537,63466,65419,67969

%N Numbers that are the sum of ten fifth powers in exactly three ways.

%C Differs from A345635 at term 19 because 55543 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5.

%H Sean A. Irvine, <a href="/A346348/b346348.txt">Table of n, a(n) for n = 1..10000</a>

%e 8194 is a term because 8194 = 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 5^5 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 4^5 + 4^5 + 4^5 + 5^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

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

%o for pos in cwr(power_terms, 10):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 3])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A345635, A345855, A346338, A346347, A346349.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jul 13 2021

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Last modified March 4 22:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)