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%I #18 May 21 2016 15:35:33
%S 40033,443889,1845649,2048391,4342914,5799339,26122131,32973759,
%T 41301953,45882739,53226297,54269091,65272753,66763333,70449093,
%U 84637287,86316741,90527229,91140435,94100426,104212017,127396178,128966383,131126303,131997229
%N Cubefree taxi-cab numbers that are not squarefree.
%C There are two versions of "taxicab numbers" that are A001235 and A011541. This sequence focuses on the version A001235.
%C This sequence lists cubefree taxi-cab numbers that are divisible by a square greater than 1.
%C Intersection of A001235 and A067259.
%C Subsequence of A272885.
%e Taxi-cab number 40033 is a term because 40033 = 7^2*19*43.
%e Taxi-cab number 443889 is a term because 443889 = 3^2*31*37*43.
%e Taxi-cab number 1845649 is a term because 1845649 = 13^2*67*163.
%o (PARI) T = thueinit(x^3+1, 1);
%o isA001235(n) = my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1;
%o isA067259(n) = n>3 && vecmax(factor(n)[, 2])==2;
%o for(n=1, 1e10, if(isA001235(n) && isA067259(n), print1(n, ", ")));
%Y Cf. A001235, A011541, A067259, A272885.
%K nonn
%O 1,1
%A _Altug Alkan_, May 09 2016
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