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 A033831 #30 Jul 02 2025 16:01:56
%S A033831 0,0,1,1,1,1,1,2,1,2,1,2,1,2,2,2,1,3,1,2,2,2,1,4,1,2,2,3,1,3,1,3,2,2,
%T A033831 2,4,1,2,2,4,1,3,1,3,3,2,1,5,1,3,2,3,1,4,2,3,2,2,1,6,1,2,3,3,2,4,1,3,
%U A033831 2,4,1,5,1,2,3,3,2,4,1,5,2,2,1,6,2,2,2,4,1,5,2,3,2,2,2,6,1,3,3,4,1,4,1,4,4
%N A033831 Number of numbers d dividing n such that d >= 3 and n/d <= d-2.
%H A033831 Nathaniel Johnston, <a href="/A033831/b033831.txt">Table of n, a(n) for n = 1..10000</a>
%F A033831 G.f.: Sum_{n>=1} x^(n^2+2*n)/(1-x^n). - _Vladeta Jovovic_, May 13 2008
%F A033831 a(n) = floor(A000005(n)/2) - 1 if n is oblong (A002378); and floor(A000005(n)/2) otherwise. - _Max Alekseyev_, Oct 09 2023
%p A033831 with(numtheory): for n from 1 to 200 do it := divisors(n): count := 0: for i from 1 to nops(it) do if it[i]>=3 and 1<=n/it[i] and n/it[i]<=(it[i]-2) then count := count+1 fi :od: printf(`%d,`,count) od:
%t A033831 a[n_] := DivisorSum[n, 1&, # > 2 && n/# < #-1 &]; Array[a, 100] (* _Amiram Eldar_, Jun 11 2019 *)
%o A033831 (PARI) a(n) = sumdiv(n, d, (d>=3) && (q=n/d) && (q>=1) && (q<=d-2)); \\ _Michel Marcus_, Nov 05 2014
%o A033831 (PARI) a033831(n) = numdiv(n)\2 - issquare(4*n+1); \\ _Max Alekseyev_, Oct 09 2023
%Y A033831 Cf. A002378.
%K A033831 easy,nonn
%O A033831 1,8
%A A033831 _Naohiro Nomoto_
%E A033831 More terms from _James Sellers_, Jun 20 2000