%I #29 Feb 23 2024 20:13:23

%S 3,17,26,99,485,577,1351,3363,19601,24335,70226,114243,470449,665857,

%T 930249,2862251,3650401,3880899,22619537,39480499,130576328,131836323,

%U 189750626,456335045,768398401,1184384449,4478554083,9863382151,10850138895,26102926097

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

%C a(31) > 10^11. - _Donovan Johnson_, Nov 15 2011

%C a(n) - 1 is a term of A335851. - _Amiram Eldar_, Feb 23 2024

%H Amiram Eldar, <a href="/A060860/b060860.txt">Table of n, a(n) for n = 1..55</a>

%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.

%F a(n) = sqrt(A060859(n) + 1). - _Amiram Eldar_, Feb 23 2024

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

%t 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 *)

%Y Cf. A060355, A060859, A001694, A335851.

%K nonn

%O 1,1

%A _Labos Elemer_, May 04 2001

%E Corrected and extended by _Jud McCranie_, Jul 08 2001

%E a(21)-a(24) from _Donovan Johnson_, Apr 27 2008

%E a(25)-a(26) from _Donovan Johnson_, Dec 07 2008

%E a(27)-a(28) from _Donovan Johnson_, Jun 17 2011

%E a(29)-a(30) from _Donovan Johnson_, Nov 15 2011