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 A363189 #9 May 21 2023 12:56:31
%S A363189 1,4,6,7,10,13,16,17,20,24,25,28,30,31,35,39,41,43,45,48,51,56,57,60,
%T A363189 62,63,65,68,71,75,79,82,83,84,87,90,94,97,98,99,102,103,105,107,110,
%U A363189 114,117,120,122,125,127,129,133,138,141,142,144,145,148,151,152
%N A363189 Indices of the odd terms in the sequence of powerful numbers (A001694).
%C A363189 The asymptotic density of this sequence is (2-sqrt(2))/(3-sqrt(2)) = 0.369398... .
%C A363189 If A001694(k) is a term of A363190 then k and k+1 are consecutive integers in this sequence.
%H A363189 Amiram Eldar, <a href="/A363189/b363189.txt">Table of n, a(n) for n = 1..10000</a>
%H A363189 Teerapat Srichan, <a href="http://www.math.nthu.edu.tw/~amen/2020/AMEN-200219.pdf">The odd/even dichotomy for the set of square-full numbers</a>, Applied Mathematics E-Notes, Vol. 20 (2020), pp. 528-531.
%H A363189 Wikipedia, <a href="https://oeis.org/A363176/b363176.txt">Powerful number</a>.
%e A363189 The first 6 powerful numbers are 1, 4, 8, 9, 16 and 25. 1, 9 and 25 are odd and their positions in the sequence are 1, 4 and 6, respectively.
%t A363189 Position[Select[Range[7000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &], _?(OddQ[#] &)] // Flatten
%o A363189 (PARI) lista(kmax) = {my(c = 0); for(k = 1, kmax, if(ispowerful(k), c++; if(k%2, print1(c, ", ")))); }
%Y A363189 Cf. A001694, A062739, A363190, A363191, A363192.
%K A363189 nonn,easy
%O A363189 1,2
%A A363189 _Amiram Eldar_, May 21 2023