A371602 Taxicab numbers that are sandwiched between squarefree numbers.

4104, 32832, 39312, 110808, 171288, 262656, 314496, 373464, 513000, 886464, 1016496, 1075032, 1195112, 1331064, 1370304, 1407672, 1609272, 1728216, 1734264, 1774656, 2101248, 2515968, 2864288, 2987712, 2991816, 3511872, 3512808, 3551112, 4104000, 4342914, 4467528, 4511808, 4607064

Offset: 1

Author

Massimo Kofler, Mar 29 2024

Keywords

• nonn

Comments

All terms are even numbers.

Examples

			4104 = 2^3 * 3^3 * 19 (between 4103 = 11 * 373 and 4105 = 5 * 821).
32832 = 2^6 * 3^3 *19 (between 32831 and 32833, which are twin primes).
39312 = 2^4 * 3^3 * 7 * 13 (between 39311 = 19 * 2069 and 39313, which is prime).
		

Links

• Christian Boyer, Les nombres Taxicabs, in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.

Crossrefs

Intersection of A001235 and A067874.

A272892 is a subsequence.

Cf. A011541, A005117.

Programs

Mathematica

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