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 A376172 #10 Sep 13 2024 11:58:51
%S A376172 1,4,9,16,25,36,49,64,72,81,100,108,121,144,169,196,200,225,256,288,
%T A376172 289,324,361,392,400,441,484,500,529,576,625,675,676,729,784,800,841,
%U A376172 900,961,968,972,1024,1089,1125,1152,1156,1225,1296,1323,1352,1369,1372,1444
%N A376172 Numbers whose prime factorization has an even minimum exponent.
%C A376172 Numbers k such that A051904(k) is even.
%C A376172 The minimum exponent in the prime factorization of 1 is considered to be A051904(1) = 0, and therefore 1 is a term of this sequence.
%H A376172 Amiram Eldar, <a href="/A376172/b376172.txt">Table of n, a(n) for n = 1..10000</a>
%H A376172 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A376172 Sum_{n>=1} 1/a(n) = 1 + Sum_{k>=1} (-1)^(k+1) * s(k) = 1.70559662202357112914..., where s(k) = Product_{p prime} (1 + 1/(p^k*(p-1))).
%t A376172 seq[lim_] := Select[Union@ Flatten@ Table[i^2 * j^3, {j, 1, Surd[lim, 3]}, {i, 1, Sqrt[lim/j^3]}], # == 1 || EvenQ[Min[FactorInteger[#][[;; , 2]]]] &]; seq[2000]
%o A376172 (PARI) is(k) = {my(f = factor(k), e = f[,2]); !(#e) || (ispowerful(f) && !(vecmin(e) % 2));}
%Y A376172 Subsequence of A001694.
%Y A376172 Complement of A376173 within A001694.
%Y A376172 Subsequences: A001248, A062503, A325240.
%Y A376172 Cf. A051904.
%K A376172 nonn,easy
%O A376172 1,2
%A A376172 _Amiram Eldar_, Sep 13 2024