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 A336177 #8 Jul 18 2020 04:32:57 %S A336177 5,11,14,22,25,33,44,46,55,58,62,70,72,73,82,88,96,98,103,104,109,110, %T A336177 111,124,129,135,155,156,158,164,172,176,178,181,187,197,203,206,207, %U A336177 209,212,218,240,243,248,249,254,257,259,268,277,279,281,285,288,291 %N A336177 Numbers k such that there are exactly two powerful numbers between k^2 and (k+1)^2. %C A336177 Positions of 2's in A119241. %C A336177 Shiu (1980) proved that this sequence has an asymptotic density 0.2312... A more accurate calculation using his formula gives 0.231299167354828... %D A336177 József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter VI, p. 226. %H A336177 Amiram Eldar, <a href="/A336177/b336177.txt">Table of n, a(n) for n = 1..10000</a> %H A336177 P. Shiu, <a href="https://doi.org/10.1112/S0025579300010056">On the number of square-full integers between successive squares</a>, Mathematika, Vol. 27, No. 2 (1980), pp. 171-178. %e A336177 5 is a term since there are exactly two powerful numbers, 27 = 3^3 and 32 = 2^5 between 5^2 = 25 and (5+1)^2 = 36. %t A336177 powQ[n_] := (n == 1) || Min @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[300], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?powQ] == 2 &] %Y A336177 Cf. A001694, A119241, A119242, A336175, A336176, A336178. %K A336177 nonn %O A336177 1,1 %A A336177 _Amiram Eldar_, Jul 10 2020