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 A369563 #10 Mar 06 2024 17:25:08
%S A369563 1,25,125,169,289,625,841,1369,1681,2197,2809,3125,3721,4225,4913,
%T A369563 5329,7225,7921,9409,10201,11881,12769,15625,18769,21025,21125,22201,
%U A369563 24389,24649,28561,29929,32761,34225,36125,37249,38809,42025,48841,50653,52441,54289,54925
%N A369563 Powerful numbers whose prime factors are all of the form 4*k + 1.
%C A369563 Closed under multiplication.
%H A369563 Amiram Eldar, <a href="/A369563/b369563.txt">Table of n, a(n) for n = 1..10000</a>
%H A369563 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A369563 Sum_{n>=1} 1/a(n) = Product_{primes p == 1 (mod 4)} (1 + 1/(p*(p-1))) = A175647 * A334424 = 1.0654356335... .
%t A369563 q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 4] == 1 && Last[#] > 1 &]; Select[Range[50000], q]
%o A369563 (PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1]%4 != 1 || f[i, 2] == 1, return(0))); 1;}
%Y A369563 Intersection of A001694 and A004613.
%Y A369563 Subsequence: A146945.
%Y A369563 Similar sequence: A352492, A369564, A369565, A369566.
%Y A369563 Cf. A002144, A008846, A175647, A334424.
%K A369563 nonn
%O A369563 1,2
%A A369563 _Amiram Eldar_, Jan 26 2024