A371602 - OEIS

%I #19 Apr 24 2024 13:30:08

%S 4104,32832,39312,110808,171288,262656,314496,373464,513000,886464,

%T 1016496,1075032,1195112,1331064,1370304,1407672,1609272,1728216,

%U 1734264,1774656,2101248,2515968,2864288,2987712,2991816,3511872,3512808,3551112,4104000,4342914,4467528,4511808,4607064

%N Taxicab numbers that are sandwiched between squarefree numbers.

%C All terms are even numbers.

%H Christian Boyer, <a href="https://medias.pourlascience.fr/api/v1/files/5a82a1e48fe56f68674f7ff2?alt=file">Les nombres Taxicabs</a>, in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.

%e 4104 = 2^3 * 3^3 * 19 (between 4103 = 11 * 373 and 4105 = 5 * 821).

%e 32832 = 2^6 * 3^3 *19 (between 32831 and 32833, which are twin primes).

%e 39312 = 2^4 * 3^3 * 7 * 13 (between 39311 = 19 * 2069 and 39313, which is prime).

%t Select[Range[300000], And @@ SquareFreeQ /@ (# + {-1, 1}) && Length[PowersRepresentations[#, 2, 3]] > 1 &] (* _Amiram Eldar_, Mar 29 2024 *)

%Y Intersection of A001235 and A067874.

%Y A272892 is a subsequence.

%Y Cf. A011541, A005117.

%K nonn

%O 1,1

%A _Massimo Kofler_, Mar 29 2024