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%I #23 May 24 2016 09:39:08
%S 1729,20683,149389,195841,327763,2418271,6058747,7620661,9443761,
%T 10765603,13623913,18406603,32114143,68007673,105997327,106243219,
%U 166560193,216226981,446686147,584504191,813357253,959281759,1098597061,1736913439,2072769211,2460483307
%N Taxi-cab numbers (A001235) that are the product of exactly three (not necessarily distinct) primes.
%C Note that the sum of two positive cubes cannot be prime except 2, obviously. Additionally, if the sum of two positive cubes is a semiprime, then, all corresponding semiprimes have a unique representation as a sum of two distinct positive cubes (see comment section of A085366). Since we know that 1729 is the first member of A001235 and it has three prime divisors, the minimum value of the number of prime divisors of a taxi-cab number must be three. This was the motivation of the definition of this sequence.
%H Chai Wah Wu, <a href="/A272935/b272935.txt">Table of n, a(n) for n = 1..131</a>
%e Taxi-cab number 1729 is a term because 1729 = 7*13*19.
%e Taxi-cab number 20683 is a term because 20683 = 13*37*43.
%e Taxi-cab number 149389 is a term because 149389 = 31*61*79.
%Y Cf. A001235, A003325, A014612, A085366.
%K nonn
%O 1,1
%A _Altug Alkan_, May 11 2016
%E a(7)-a(26) from _Chai Wah Wu_, May 22 2016