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 A191219 #13 Sep 30 2018 13:47:03 %S A191219 5,9,13,41,49,61,113,121,169,181,225,289,313,421,441,613,625,761,925, %T A191219 1013,1201,1301,1521,1681,1741,1849,1861,2025,2113,2381,2401,2521, %U A191219 3121,3481,3613,3969,4325,4513,4761,4901 %N A191219 Positive integers k such that n=k*(2*k-1) satisfies: sigma(n) congruent to 2 modulo 4. %C A191219 If there are odd perfect numbers n of the form n=k*(2*k-1) the corresponding k should appear in this sequence. The sequence has no even terms. %H A191219 Harvey P. Dale, <a href="/A191219/b191219.txt">Table of n, a(n) for n = 1..700</a> %e A191219 For n=4, a(4) = 41 since n = 41*(82 -1) = 3321 and sigma(3321)= 5082 = 4*1270 +2. %p A191219 with(numtheory): genz := proc(b)local z,n,s,d; for z from 1 to b by 2 do n := z*(2*z-1); s := sigma(n); if modp(n,4)=2 then print(z); fi; od; end; %t A191219 Select[Range[1,5001,2],Mod[DivisorSigma[1,#(2#-1)],4]==2&] (* _Harvey P. Dale_, Sep 30 2018 *) %K A191219 nonn %O A191219 1,1 %A A191219 _Luis H. Gallardo_, May 26 2011