login
A272889
Cubefree taxi-cab numbers that are not squarefree.
0
40033, 443889, 1845649, 2048391, 4342914, 5799339, 26122131, 32973759, 41301953, 45882739, 53226297, 54269091, 65272753, 66763333, 70449093, 84637287, 86316741, 90527229, 91140435, 94100426, 104212017, 127396178, 128966383, 131126303, 131997229
OFFSET
1,1
COMMENTS
There are two versions of "taxicab numbers" that are A001235 and A011541. This sequence focuses on the version A001235.
This sequence lists cubefree taxi-cab numbers that are divisible by a square greater than 1.
Intersection of A001235 and A067259.
Subsequence of A272885.
EXAMPLE
Taxi-cab number 40033 is a term because 40033 = 7^2*19*43.
Taxi-cab number 443889 is a term because 443889 = 3^2*31*37*43.
Taxi-cab number 1845649 is a term because 1845649 = 13^2*67*163.
PROG
(PARI) T = thueinit(x^3+1, 1);
isA001235(n) = my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1;
isA067259(n) = n>3 && vecmax(factor(n)[, 2])==2;
for(n=1, 1e10, if(isA001235(n) && isA067259(n), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, May 09 2016
STATUS
approved