A370693 Cubes sandwiched between squarefree numbers.

216, 1728, 46656, 74088, 157464, 216000, 287496, 373248, 474552, 592704, 729000, 884736, 1061208, 1259712, 1481544, 2299968, 2628072, 2985984, 3375000, 3796416, 4251528, 5832000, 6434856, 7762392, 8489664, 9261000, 10077696, 10941048, 11852352, 12812904, 13824000, 16003008, 17173512, 19683000

Offset

1,1

Comments

All terms are multiples of 216.

Links

Table of n, a(n) for n=1..34.

Example

216 = 2^3 * 3^3 is a cube; 215 = 5 * 43 and 217 = 7 * 31 are squarefree, so 216 is a term.
1728 = 2^6 * 3^3 is a cube; 1727 = 11 * 157 and 1729 = 7 * 13 * 19 are squarefree, so 1728 is a term.
46656 = 2^6 * 3^6 is a cube; 46655 = 5 * 7 * 31 * 43 and 46657 = 13 * 37 * 97 are squarefree, so 46656 is a term.

Mathematica

Select[Range[270]^3, And @@ SquareFreeQ /@ (# + {-1, 1}) &] (* Amiram Eldar, Feb 27 2024 *)

Crossrefs

Cf. A005117. Subsequence of A000578.

Sequence in context: A033698 A121683 A016911 * A323801 A222694 A243862

Adjacent sequences: A370690 A370691 A370692 * A370694 A370695 A370696

Keyword

nonn

Author

Massimo Kofler, Feb 27 2024

Status

approved