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 A333749 #20 Mar 02 2021 09:21:31
%S A333749 1,1,1,2,1,2,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,2,2,2,2,1,4,1,2,2,2,
%T A333749 2,4,1,2,2,3,1,4,1,2,3,2,1,4,2,3,2,2,1,4,2,3,2,2,1,5,1,2,3,2,2,4,1,2,
%U A333749 2,4,1,4,1,2,3,2,2,4,1,3,2,2,1,5,2,2,2,2,1,5,2,2,2,2,2,4,1,3,2,4
%N A333749 Number of squarefree divisors of n that are <= sqrt(n).
%C A333749 If we define a divisor d|n to be inferior if d <= n/d, then inferior divisors are counted by A038548 and listed by A161906. This sequence counts inferior squarefree divisors. - _Gus Wiseman_, Feb 27 2021
%H A333749 Robert Israel, <a href="/A333749/b333749.txt">Table of n, a(n) for n = 1..10000</a>
%F A333749 G.f.: Sum_{k>=1} mu(k)^2 * x^(k^2) / (1 - x^k).
%e A333749 n inferior squarefree divisors of n
%e A333749 --- ---------------------------------
%e A333749 33 1, 3
%e A333749 56 1, 2, 7
%e A333749 429 1, 3, 11, 13
%e A333749 90 1, 2, 3, 5, 6
%e A333749 490 1, 2, 5, 7, 10, 14
%e A333749 480 1, 2, 3, 5, 6, 10, 15
%p A333749 N:= 200: # for a(1)..a(N)
%p A333749 g:= add(x^(k^2)/(1-x^k), k = select(numtheory:-issqrfree,[$1..floor(sqrt(N))])):
%p A333749 S:= series(g,x,N+1):
%p A333749 seq(coeff(S,x,j),j=1..N); # _Robert Israel_, Apr 05 2020
%t A333749 Table[DivisorSum[n, 1 &, # <= Sqrt[n] && SquareFreeQ[#] &], {n, 1, 100}]
%t A333749 nmax = 100; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A333749 (PARI) a(n) = sumdiv(n, d, (d^2<=n) && issquarefree(d)); \\ _Michel Marcus_, Apr 03 2020
%Y A333749 Cf. A034444, A069291, A333748, A333752.
%Y A333749 Positions of 1's are A008578.
%Y A333749 The case of equality is the indicator function of A062503.
%Y A333749 The version for prime instead of squarefree divisors is A063962.
%Y A333749 The version for odd instead of squarefree divisors is A069288.
%Y A333749 The version for prime-power instead of squarefree divisors is A333750.
%Y A333749 The superior version is A341592.
%Y A333749 The strictly superior version is A341595.
%Y A333749 The strictly inferior version is A341596.
%Y A333749 A005117 lists squarefree numbers.
%Y A333749 A038548 counts superior (or inferior) divisors.
%Y A333749 A056924 counts strictly superior (or strictly inferior) divisors.
%Y A333749 A161906 lists inferior divisors.
%Y A333749 A161908 lists superior divisors.
%Y A333749 A207375 list central divisors.
%Y A333749 - Inferior: A033676, A066839, A217581.
%Y A333749 - Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A341593, A341675, A341676.
%Y A333749 - Strictly Inferior: A060775, A070039, A333805, A333806, A341674, A341677.
%Y A333749 - Strictly Superior: A048098, A064052 A140271, A238535, A341591, A341594, A341642, A341643, A341644, A341645/A341646, A341673.
%Y A333749 Cf. A000005, A000203, A001221, A001222, A001248, A006530, A020639.
%K A333749 nonn
%O A333749 1,4
%A A333749 _Ilya Gutkovskiy_, Apr 03 2020