A060860 Numbers k such that k^2-1 and k^2 are consecutive powerful numbers.

3, 17, 26, 99, 485, 577, 1351, 3363, 19601, 24335, 70226, 114243, 470449, 665857, 930249, 2862251, 3650401, 3880899, 22619537, 39480499, 130576328, 131836323, 189750626, 456335045, 768398401, 1184384449, 4478554083, 9863382151, 10850138895, 26102926097

Offset

1,1

Comments

a(31) > 10^11. - Donovan Johnson, Nov 15 2011

a(n) - 1 is a term of A335851. - Amiram Eldar, Feb 23 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..55

Index entries for sequences related to powerful numbers.

Formula

a(n) = sqrt(A060859(n) + 1). - Amiram Eldar, Feb 23 2024

Example

592192224 = 2^5*3^2*13^2*23^3 = 24334*24336, 592192225 = 5^2*31^2*157^2 = 24335^2.

Mathematica

seq[max_] := Module[{p = Union[Flatten[Table[i^2*j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}]]], q, i}, q = Union[p, 2*Select[p, # <= max && OddQ[#] &]]; i = Position[Differences[q], 2] // Flatten; Sqrt[q[[i]]*(q[[i]] + 2) + 1]]; seq[10^10] (* Amiram Eldar, Feb 23 2024 *)

Crossrefs

Cf. A060355, A060859, A001694, A335851.

Sequence in context: A174268 A273834 A273850 * A273782 A101153 A192538

Adjacent sequences: A060857 A060858 A060859 * A060861 A060862 A060863

Keyword

nonn

Author

Labos Elemer, May 04 2001

Extensions

Corrected and extended by Jud McCranie, Jul 08 2001

a(21)-a(24) from Donovan Johnson, Apr 27 2008

a(25)-a(26) from Donovan Johnson, Dec 07 2008

a(27)-a(28) from Donovan Johnson, Jun 17 2011

a(29)-a(30) from Donovan Johnson, Nov 15 2011

Status

approved