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 A333805 #25 Nov 02 2022 16:51:18
%S A333805 0,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,3,1,1,2,1,
%T A333805 2,2,1,1,2,2,1,2,1,1,3,1,1,2,1,2,2,1,1,2,2,2,2,1,1,3,1,1,3,1,2,2,1,1,
%U A333805 2,3,1,2,1,1,3,1,2,2,1,2,2,1,1,3,2,1,2,1,1,4,2,1,2,1,2,2,1,2,3,2,1,2,1,1,4
%N A333805 Number of odd divisors of n that are < sqrt(n).
%C A333805 If we define a divisor d|n to be strictly inferior if d < n/d, then strictly inferior divisors are counted by A056924 and listed by A341674. This sequence counts strictly inferior odd divisors. - _Gus Wiseman_, Feb 26 2021
%H A333805 Antti Karttunen, <a href="/A333805/b333805.txt">Table of n, a(n) for n = 1..65537</a>
%F A333805 G.f.: Sum_{k>=1} x^(2*k*(2*k - 1)) / (1 - x^(2*k - 1)).
%e A333805 The strictly inferior odd divisors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, so a(945) = 8. - _Gus Wiseman_, Feb 27 2021
%t A333805 Table[DivisorSum[n, 1 &, # < Sqrt[n] && OddQ[#] &], {n, 1, 90}]
%t A333805 nmax = 90; CoefficientList[Series[Sum[x^(2 k (2 k - 1))/(1 - x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A333805 (PARI) A333805(n) = sumdiv(n,d,(d%2)&&((d*d)<n)); \\ _Antti Karttunen_, Nov 02 2022
%Y A333805 Dominated by A001227 (number of odd divisors).
%Y A333805 Strictly inferior divisors (not just odd) are counted by A056924.
%Y A333805 The non-strict version is A069288.
%Y A333805 These divisors add up to A070039.
%Y A333805 The case of prime divisors is A333806.
%Y A333805 The strictly superior version is A341594.
%Y A333805 The case of squarefree divisors is A341596.
%Y A333805 The superior version is A341675.
%Y A333805 The case of prime-power divisors is A341677.
%Y A333805 A006530 selects the greatest prime factor.
%Y A333805 A020639 selects the smallest prime factor.
%Y A333805 - Odd -
%Y A333805 A000009 counts partitions into odd parts, ranked by A066208.
%Y A333805 A026424 lists numbers with odd Omega.
%Y A333805 A027193 counts odd-length partitions.
%Y A333805 A067659 counts strict partitions of odd length, ranked by A030059.
%Y A333805 - Inferior divisors -
%Y A333805 A033676 selects the greatest inferior divisor.
%Y A333805 A033677 selects the smallest superior divisor.
%Y A333805 A038548 counts superior (or inferior) divisors.
%Y A333805 A060775 selects the greatest strictly inferior divisor.
%Y A333805 A341674 lists strictly inferior divisors.
%Y A333805 Cf. A001248, A051283, A063538/A063539, A063962, A116883/A116882, A300272, A333807, A333809, A340832.
%K A333805 nonn
%O A333805 1,12
%A A333805 _Ilya Gutkovskiy_, Apr 05 2020
%E A333805 Data section extended up to a(105) by _Antti Karttunen_, Nov 02 2022