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 A369565 #7 Jan 26 2024 08:34:56
%S A369565 1,49,169,343,361,961,1369,1849,2197,2401,3721,4489,5329,6241,6859,
%T A369565 8281,9409,10609,11881,16129,16807,17689,19321,22801,24649,26569,
%U A369565 28561,29791,32761,37249,39601,44521,47089,49729,50653,52441,57967,58081,61009,67081,73441
%N A369565 Powerful numbers whose prime factors are all of the form 3*k + 1.
%C A369565 Closed under multiplication.
%H A369565 Amiram Eldar, <a href="/A369565/b369565.txt">Table of n, a(n) for n = 1..10000</a>
%H A369565 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A369565 Sum_{n>=1} 1/a(n) = Product_{primes p == 1 (mod 3)} (1 + 1/(p*(p-1))) = A175646 * A334477 = 1.0377399555...
%t A369565 q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 3] == 1 && Last[#] > 1 &]; Select[Range[75000], q]
%o A369565 (PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1]%3 != 1 || f[i, 2] == 1, return(0))); 1;}
%Y A369565 Intersection of A001694 and A004611.
%Y A369565 Similar sequence: A352492, A369563, A369564, A369566.
%Y A369565 Cf. A002476, A175646, A334477.
%K A369565 nonn
%O A369565 1,2
%A A369565 _Amiram Eldar_, Jan 26 2024