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 A377819 #12 Nov 09 2024 16:17:47
%S A377819 1,4,8,9,16,25,27,32,49,64,72,81,108,121,125,128,169,200,216,243,256,
%T A377819 288,289,343,361,392,432,500,512,529,625,648,675,729,800,841,864,961,
%U A377819 968,972,1000,1024,1125,1152,1323,1331,1352,1369,1372,1568,1681,1728,1849,1944,2000
%N A377819 Powerful numbers that have no more than one even exponent in their prime factorization.
%C A377819 Powerful numbers k such that A350388(k) is either 1 or a prime power with an even positive exponent (A056798 \ {1}).
%H A377819 Amiram Eldar, <a href="/A377819/b377819.txt">Table of n, a(n) for n = 1..10000</a>
%H A377819 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A377819 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p*(p^2-1))) * (1 + Sum_{p prime} (p/(p^3-p+1))) = 1.84528389659572754387... .
%t A377819 With[{max = 2000}, Select[Union@ Flatten@Table[i^2 * j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}], Count[FactorInteger[#][[;; , 2]], _?EvenQ] <= 1 &]]
%o A377819 (PARI) is(k) = if(k == 1, 1, my(e = factor(k)[, 2]); vecmin(e) > 1 && #select(x -> !(x%2), e) <= 1);
%Y A377819 Disjoint union of A335988 and A377818.
%Y A377819 Intersection of A001694 and the complement of A377817.
%Y A377819 Cf. A056798, A065487, A350388.
%K A377819 nonn,easy
%O A377819 1,2
%A A377819 _Amiram Eldar_, Nov 09 2024