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A345865 Numbers that are the sum of two cubes in exactly four ways.

%I A345865 #6 Jul 31 2021 23:46:55
%S A345865 6963472309248,12625136269928,21131226514944,26059452841000,
%T A345865 55707778473984,74213505639000,95773976104625,101001090159424,
%U A345865 159380205560856,169049812119552,174396242861568,188013752349696,208475622728000,300656502205416,340878679288056
%N A345865 Numbers that are the sum of two cubes in exactly four ways.
%C A345865 Differs from A023051 at term 143 because 48988659276962496 = 331954^3 + 231518^3 = 336588^3 + 221424^3 = 342952^3 + 205292^3 = 362753^3 + 107839^3 = 365757^3 + 38787^3.
%H A345865 Sean A. Irvine, <a href="/A345865/b345865.txt">Table of n, a(n) for n = 1..154</a>
%e A345865 12625136269928 is a term because 12625136269928 = 21869^3 + 12939^3 = 22580^3 + 10362^3 = 23066^3 + 7068^3 = 23237^3 + 4275^3.
%o A345865 (Python)
%o A345865 from itertools import combinations_with_replacement as cwr
%o A345865 from collections import defaultdict
%o A345865 keep = defaultdict(lambda: 0)
%o A345865 power_terms = [x**3 for x in range(1, 1000)]
%o A345865 for pos in cwr(power_terms, 2):
%o A345865     tot = sum(pos)
%o A345865     keep[tot] += 1
%o A345865     rets = sorted([k for k, v in keep.items() if v == 4])
%o A345865     for x in range(len(rets)):
%o A345865         print(rets[x])
%Y A345865 Cf. A023051, A025287, A343969, A344804.
%K A345865 nonn
%O A345865 1,1
%A A345865 _David Consiglio, Jr._, Jul 05 2021