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

Author

Labos Elemer, May 04 2001

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..55
• Index entries for sequences related to powerful numbers.

Crossrefs

Cf. A060355, A060859, A001694, A335851.

Programs

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 *)

Formula

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

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