This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365983 #36 Mar 28 2025 03:26:00
%S A365983 26,70226,130576328,189750626,512706121226,13837575261124,
%T A365983 99612037019890,1385331749802026
%N A365983 Even numbers k such that k^2 - 1 is a powerful number.
%C A365983 This sequence is a subsequence of A060860 (the even terms) and a supersequence of A094835. All the terms of A094835 are in this sequence, but 130576328 is not in A094835. A094835 also shows that this sequence is infinite.
%C A365983 Terms A076445(n)+1 are terms of this sequence because A076445(n) and A076445(n)+2 are powerful and (A076445(n)+1)^2-1 = A076445(n) * (A076445(n)+2), which is also powerful.
%C A365983 a(n) - 1 is an odd powerful number (A062739). - _Amiram Eldar_, Feb 23 2024
%D A365983 Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, entries 70226 and 485.
%H A365983 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%e A365983 26^2 - 1 = 675 = 3^3 * 5^2 is powerful.
%e A365983 130576328^2 - 1 = 17050177433963583 = 3^2 * 7^3 * 13^2 * 293^2 * 617^2, whose exponents are all greater than 1, so it is powerful.
%t A365983 seq[max_] := Module[{p = Union[Flatten[Table[i^2*j^3, {j, 1, max^(1/3), 2}, {i, 1, Sqrt[max/j^3], 2}]]], i}, i = Position[Differences[p], 2] // Flatten; Sqrt[p[[i]]*(p[[i]] + 2) + 1]]; seq[10^10] (* _Amiram Eldar_, Feb 23 2024 *)
%o A365983 (PARI) isok(k) = !(k%2) && ispowerful(k^2-1); \\ _Michel Marcus_, Sep 25 2023
%Y A365983 Cf. A000466, A001694, A062739, A094835, A060860, A076445.
%K A365983 nonn,more
%O A365983 1,1
%A A365983 _Jud McCranie_, Sep 24 2023
%E A365983 a(5)-a(8) from _Amiram Eldar_, Feb 23 2024