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 A369566 #7 Jan 26 2024 08:35:02
%S A369566 1,4,8,16,25,32,64,100,121,125,128,200,256,289,400,484,500,512,529,
%T A369566 625,800,841,968,1000,1024,1156,1331,1600,1681,1936,2000,2048,2116,
%U A369566 2209,2312,2500,2809,3025,3125,3200,3364,3481,3872,4000,4096,4232,4624,4913,5000
%N A369566 Powerful numbers whose prime factors are all of the form 3*k + 2.
%C A369566 Closed under multiplication.
%H A369566 Amiram Eldar, <a href="/A369566/b369566.txt">Table of n, a(n) for n = 1..10000</a>
%H A369566 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A369566 Sum_{n>=1} 1/a(n) = Product_{primes p == 2 (mod 3)} (1 + 1/(p*(p-1))) = (9/8) * A333240 * A334479 = 1.6053538210...
%t A369566 q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 3] == 2 && Last[#] > 1 &]; Select[Range[5000], q]
%o A369566 (PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1]%3 != 2 || f[i, 2] == 1, return(0))); 1;}
%Y A369566 Intersection of A001694 and A004612.
%Y A369566 Similar sequence: A352492, A369563, A369564, A369565.
%Y A369566 Cf. A003627, A333240, A334479.
%K A369566 nonn
%O A369566 1,2
%A A369566 _Amiram Eldar_, Jan 26 2024