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%I #12 Jul 29 2023 13:57:02
%S 51445,876733,1646240,3558289,4062500,5687000,7962869,8227494,9792364,
%T 9924675,10908544,12501135,15249850,18317994,18804544,20611151,
%U 20983875,21297837,23944908,24201342,24598407,27806867,28055456,29480343,31584102,32557875,32814683,35469555,40882844,45177175
%N Numbers that are the sum of four fifth powers in exactly two ways.
%C Differs from A344644 at term 508 because 1479604544 = 3^5 + 49^5 + 53^5 + 62^5 = 14^5 + 37^5 + 52^5 + 65^5 = 19^5 + 37^5 + 45^5 + 67^5
%H David Consiglio, Jr., <a href="/A344645/b344645.txt">Table of n, a(n) for n = 1..20000</a>
%e 1646240 is a term because 1646240 = 9^5 + 15^5 + 15^5 + 15^5 = 11^5 + 13^5 + 13^5 + 17^5
%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, 500)]
%o for pos in cwr(power_terms, 4):
%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, A344193, A344642, A344644.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, May 25 2021
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