A346357 - OEIS

%I #6 Jul 31 2021 19:24:09

%S 4098,4129,4340,5121,7222,11873,20904,36865,51447,51478,51509,51689,

%T 51720,51931,52470,52501,52712,53493,54571,54602,54813,55594,57695,

%U 59222,59253,59464,60245,62346,63146,66997,67586,68253,68284,68495,68906,68937,69148,69276

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

%C 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.

%H Sean A. Irvine, <a href="/A346357/b346357.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%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, 6):

%o     tot = sum(pos)

%o     keep[tot] += 1

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

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

%o         print(rets[x])

%Y Cf. A342686, A345507, A345814, A346279, A346356, A346358.

%K nonn

%O 1,1

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