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

1,1

Comments

All terms are even numbers.

Links

Table of n, a(n) for n=1..33.

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

Example

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).

Mathematica

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

Crossrefs

Intersection of A001235 and A067874.

A272892 is a subsequence.

Cf. A011541, A005117.

Sequence in context: A346347 A227915 A379466 * A372848 A168345 A255158

Adjacent sequences: A371599 A371600 A371601 * A371603 A371604 A371605

Keyword

nonn

Author

Massimo Kofler, Mar 29 2024

Status

approved