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 A069288 #29 Feb 13 2021 14:37:06
%S A069288 1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,2,1,2,1,1,3,1,1,2,1,
%T A069288 2,2,1,1,2,2,1,2,1,1,3,1,1,2,2,2,2,1,1,2,2,2,2,1,1,3,1,1,3,1,2,2,1,1,
%U A069288 2,3,1,2,1,1,3,1,2,2,1,2,3,1,1,3,2,1,2,1,1,4
%N A069288 Number of odd divisors of n <= sqrt(n).
%C A069288 a(n) = #{d : d = A182469(n,k), d <= A000196(n), k=1..A001227(n)}. - _Reinhard Zumkeller_, Apr 05 2015
%H A069288 Reinhard Zumkeller, <a href="/A069288/b069288.txt">Table of n, a(n) for n = 1..10000</a>
%F A069288 G.f.: Sum_{n>=1} 1/(1-q^(2*n-1)) * q^((2*n-1)^2). [_Joerg Arndt_, Mar 04 2010]
%e A069288 From _Gus Wiseman_, Feb 11 2021: (Start)
%e A069288 The inferior odd divisors for selected n are the columns below:
%e A069288 n: 1 9 30 90 225 315 630 945 1575 2835 4410 3465 8190 6930
%e A069288 --------------------------------------------------------------------
%e A069288 1 3 5 9 15 15 21 27 35 45 63 55 65 77
%e A069288 1 3 5 9 9 15 21 25 35 49 45 63 63
%e A069288 1 3 5 7 9 15 21 27 45 35 45 55
%e A069288 1 3 5 7 9 15 21 35 33 39 45
%e A069288 1 3 5 7 9 15 21 21 35 35
%e A069288 1 3 5 7 9 15 15 21 33
%e A069288 1 3 5 7 9 11 15 21
%e A069288 1 3 5 7 9 13 15
%e A069288 1 3 5 7 9 11
%e A069288 1 3 5 7 9
%e A069288 1 3 5 7
%e A069288 1 3 5
%e A069288 1 3
%e A069288 1
%e A069288 (End)
%t A069288 odn[n_]:=Count[Divisors[n],_?(OddQ[#]&&#<=Sqrt[n ]&)]; Array[odn,100] (* _Harvey P. Dale_, Nov 04 2017 *)
%o A069288 (PARI) a(n) = my(ir = sqrtint(n)); sumdiv(n, d, (d % 2) * (d <= ir)); \\ _Michel Marcus_, Jan 14 2014
%o A069288 (Haskell)
%o A069288 a069288 n = length $ takeWhile (<= a000196 n) $ a182469_row n
%o A069288 -- _Reinhard Zumkeller_, Apr 05 2015
%Y A069288 Cf. A000005, A000196, A001227, A069289, A182469.
%Y A069288 Positions of first appearances are A334853.
%Y A069288 A055396 selects the least prime index.
%Y A069288 A061395 selects the greatest prime index.
%Y A069288 - Odd -
%Y A069288 A000009 counts partitions into odd parts (A066208).
%Y A069288 A026424 lists numbers with odd Omega.
%Y A069288 A027193 counts odd-length partitions.
%Y A069288 A067659 counts strict partitions of odd length (A030059).
%Y A069288 - Inferior divisors -
%Y A069288 A033676 selects the greatest inferior divisor.
%Y A069288 A033677 selects the least superior divisor.
%Y A069288 A038548 counts inferior divisors.
%Y A069288 A060775 selects the greatest strictly inferior divisor.
%Y A069288 A063538 lists numbers with a superior prime divisor.
%Y A069288 A063539 lists numbers without a superior prime divisor.
%Y A069288 A063962 counts inferior prime divisors.
%Y A069288 A064052 lists numbers with a properly superior prime divisor.
%Y A069288 A140271 selects the least properly superior divisor.
%Y A069288 A217581 selects the greatest inferior divisor.
%Y A069288 A333806 counts strictly inferior prime divisors.
%Y A069288 Cf. A001055, A244991, A300272, A340101, A340607, A340832, A340854/A340855.
%K A069288 nonn
%O A069288 1,9
%A A069288 _Reinhard Zumkeller_, Mar 14 2002