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 A349062 #15 Mar 14 2024 11:13:08
%S A349062 1,4,9,16,36,49,81,144,169,256,289,441,529,576,676,729,900,1024,1156,
%T A349062 1225,1372,1444,1600,1849,2209,2401,2916,3600,3721,4096,4356,4624,
%U A349062 4761,5041,5625,6400,6561,7225,7396,8281,9025,9409,9801,11025,11236,11664,12544,14400
%N A349062 Powerful numbers (A001694) with a record gap to the next powerful number.
%C A349062 This sequence is infinite since the asymptotic density of the powerful numbers is 0.
%C A349062 The corresponding record gaps are 3, 4, 7, 9, 13, 15, 19, 25, 27, 32, 35, 43, ...
%C A349062 Apparently, most of the terms are squares. The nonsquare terms are 1372, 465125, 4879688, ... (A371191).
%H A349062 Amiram Eldar, <a href="/A349062/b349062.txt">Table of n, a(n) for n = 1..10000</a>
%H A349062 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%e A349062 The sequence of powerful numbers begins with 1, 4, 8, 9, 16, 25, 27, 32, 36 and 49. The differences between these terms are 3, 4, 1, 7, 9, 2, 5, 4 and 13. The record values, 3, 4, 7, 9 and 13 occur after the powerful numbers 1, 4, 9, 16 and 36, the first 5 terms of this sequence.
%t A349062 powQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 1; seq[nmax_] := Module[{s = {}, n1 = 1, gapmax = 0, gap}, Do[If[powQ[n], gap = n - n1; If[gap > gapmax, gapmax = gap; AppendTo[s, n1]]; n1 = n], {n, 2, nmax}]; s]; seq[10^5]
%Y A349062 Cf. A001694, A060355, A076445, A371191.
%K A349062 nonn
%O A349062 1,2
%A A349062 _Amiram Eldar_, Nov 07 2021