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 A377818 #12 Nov 09 2024 16:17:59
%S A377818 4,9,16,25,49,64,72,81,108,121,169,200,256,288,289,361,392,432,500,
%T A377818 529,625,648,675,729,800,841,961,968,972,1024,1125,1152,1323,1352,
%U A377818 1369,1372,1568,1681,1728,1849,2000,2209,2312,2401,2592,2809,2888,3087,3200,3267,3481
%N A377818 Powerful numbers that have a single even exponent in their prime factorization.
%C A377818 Each term can be represented in a unique way as m * p^(2*k), k >= 1, where m is a cubefull exponentially odd number (A335988) and p is a prime that does not divide m.
%C A377818 Powerful numbers k such that A350388(k) is a prime power with an even positive exponent (A056798 \ {1}).
%H A377818 Amiram Eldar, <a href="/A377818/b377818.txt">Table of n, a(n) for n = 1..10000</a>
%H A377818 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A377818 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p*(p^2-1))) * Sum_{p prime} (p/(p^3-p+1)) = 0.61399274770712398109... .
%t A377818 With[{max = 3500}, 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 A377818 (PARI) is(k) = if(k == 1, 0, my(e = factor(k)[, 2]); vecmin(e) > 1 && #select(x -> !(x%2), e) == 1);
%Y A377818 Intersection of A001694 and A377816.
%Y A377818 Subsequence of A377819.
%Y A377818 Cf. A056798, A065487, A335988, A350388.
%K A377818 nonn,easy
%O A377818 1,1
%A A377818 _Amiram Eldar_, Nov 09 2024