A088068 -id:A088068 - cp's OEIS frontend

A088069 Cubes sandwiched between two numbers divisible by cubes > 1.

4913, 6859, 166375, 704969, 2048383, 4173281, 7880599, 12649337, 15438249, 15813251, 19902511, 28372625, 34328125, 40353607, 53582633, 71473375, 90518849, 115501303, 141420761, 174676879, 208527857, 251239591, 294079625

Offset: 1

Amarnath Murthy, Sep 22 2003

nonn

Sequence is infinite. If k is a member then so is k^3. Subsidiary sequence: fourth powers sandwiched between two numbers divisible by fourth powers.

			4913 = 17^3 is a term since 4912 is divisible by 8 and 4914 is divisible by 27.

Subsequence of A088035.

Cf. A088068.

Select[Range[2, 1000], Last[Union[Transpose[FactorInteger[ #^3 - 1]][[2]]]] > 2 && Last[Union[Transpose[FactorInteger[ #^3 + 1]][[2]]]] > 2 &]^3 (* Tanya Khovanova, Sep 08 2007 *)

Corrected and extended by Ray Chandler, Sep 27 2003

Offset changed by Andrew Howroyd, Sep 22 2024

A233409 Squares with squarefree neighbors.

Original entry on oeis.org

4, 16, 36, 144, 196, 256, 400, 484, 900, 1156, 1296, 1600, 1764, 2704, 2916, 3136, 3364, 3600, 4356, 5184, 6084, 7056, 7396, 7744, 8100, 8464, 8836, 9216, 10404, 10816, 11236, 11664, 12100, 12544, 12996, 16384, 16900, 19044, 19600, 20164, 20736, 22500

Offset: 1

Irina Gerasimova, Dec 09 2013

nonn

All terms are multiples of 4. Whether n is congruent to 1 or 3 mod 4, n^2 is congruent to 1 mod 3 and therefore mu(n^2 - 1) = 0. - Alonso del Arte, Dec 12 2013

			36 is in this sequence because 35 and 37 are both squarefree.
64 is not in this sequence because 63 = 3^2 * 7.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000290, A005117, A088068.

Select[Table[n^2, {n, 150}], SquareFreeQ[# - 1] && SquareFreeQ[# + 1] &] (* Vaclav Kotesovec, Dec 11 2013 *)
Select[Range[150]^2, Abs[MoebiusMu[# - 1] MoebiusMu[# + 1]] == 1 &] (* Alonso del Arte, Dec 11 2013 *)
SequencePosition[Table[Which[IntegerQ[Sqrt[n]],1,SquareFreeQ[n],2,True,0],{n,25000}],{2,1,2}][[;;,1]]+1 (* Harvey P. Dale, Jun 27 2023 *)

forstep(n=2,1e3,[2, 2, 6, 2, 2, 2, 2],if(issquarefree(n-1) && issquarefree(n+1) && issquarefree(n^2+1), print1(n^2", "))) \\ Charles R Greathouse IV, Mar 18 2014

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A088069 Cubes sandwiched between two numbers divisible by cubes > 1.

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