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 A364357 #33 Apr 27 2025 03:23:03
%S A364357 0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,2,0,1,0,1,
%T A364357 1,1,0,1,0,2,0,1,0,1,1,1,0,1,0,2,0,1,0,1,1,1,0,1,0,2,0,1,0,2,1,1,0,1,
%U A364357 0,2,0,2,0,1,1,1,0,1,0,3,0,1,0,1,1,1,0,2,0,2,0,1,0,1,1,2,0,1,0,2
%N A364357 Number of divisors of n of the form 3*k+2 that are at most sqrt(n).
%H A364357 Robert Israel, <a href="/A364357/b364357.txt">Table of n, a(n) for n = 1..10000</a>
%F A364357 G.f.: Sum_{k>=0} x^((3*k+2)^2) / (1 - x^(3*k+2)).
%p A364357 N:= 100: # for a(1) .. a(N)
%p A364357 M:= floor((sqrt(N)-3)/2):
%p A364357 G:= series(add(x^((3*k+2)^2)/(1-x^(3*k+2)),k=0..M),x,N+1):
%p A364357 seq(coeff(G,x,i),i=1..N); # _Robert Israel_, Jun 05 2024
%t A364357 Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{2}, Mod[#, 3]] &)], {n, 100}]
%t A364357 nmax = 100; CoefficientList[Series[Sum[x^(3 k + 2)^2/(1 - x^(3 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest
%Y A364357 Cf. A001822, A038548, A364209.
%K A364357 nonn
%O A364357 1,30
%A A364357 _Ilya Gutkovskiy_, Jul 21 2023