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 A063962 #32 Mar 07 2021 19:04:44
%S A063962 0,0,0,1,0,1,0,1,1,1,0,2,0,1,1,1,0,2,0,1,1,1,0,2,1,1,1,1,0,3,0,1,1,1,
%T A063962 1,2,0,1,1,2,0,2,0,1,2,1,0,2,1,2,1,1,0,2,1,2,1,1,0,3,0,1,2,1,1,2,0,1,
%U A063962 1,3,0,2,0,1,2,1,1,2,0,2,1,1,0,3,1,1,1,1,0,3,1,1,1,1,1,2,0,2,1,2,0,2,0,1,3
%N A063962 Number of distinct prime divisors of n that are <= sqrt(n).
%C A063962 For all primes p: a(p) = 0 (not marked) and for k > 1 a(p^k) = 1.
%C A063962 a(1) = 0 and for n > 0 a(n) is the number of marks when applying the sieve of Eratosthenes where a stage for prime p starts at p^2.
%C A063962 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 prime divisors. - _Gus Wiseman_, Feb 25 2021
%H A063962 Harry J. Smith, <a href="/A063962/b063962.txt">Table of n, a(n) for n = 1..1000</a>
%F A063962 G.f.: Sum_{k>=1} x^(prime(k)^2) / (1 - x^prime(k)). - _Ilya Gutkovskiy_, Apr 04 2020
%F A063962 a(A002110(n)) = n for n > 2. - _Gus Wiseman_, Feb 25 2021
%e A063962 a(33) = a(3*11) = 1, as 3^2 = 9 < 33 and 11^2 = 121 > 33.
%e A063962 From _Gus Wiseman_, Feb 25 2021: (Start)
%e A063962 The a(n) inferior prime divisors (columns) for selected n:
%e A063962 n = 3 8 24 3660 390 3570 87780
%e A063962 ---------------------------------
%e A063962 {} 2 2 2 2 2 2
%e A063962 3 3 3 3 3
%e A063962 5 5 5 5
%e A063962 13 7 7
%e A063962 17 11
%e A063962 19
%e A063962 (End)
%p A063962 with(numtheory): a:=proc(n) local c,F,f,i: c:=0: F:=factorset(n): f:=nops(F): for i from 1 to f do if F[i]^2<=n then c:=c+1 else c:=c: fi od: c; end: seq(a(n),n=1..105); # _Emeric Deutsch_
%t A063962 Join[{0},Table[Count[Transpose[FactorInteger[n]][[1]],_?(#<=Sqrt[n]&)],{n,2,110}]] (* _Harvey P. Dale_, Mar 26 2015 *)
%o A063962 (PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[1, i]^2<=n, a++, break)); write("b063962.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 04 2009
%o A063962 (Haskell)
%o A063962 a063962 n = length [p | p <- a027748_row n, p ^ 2 <= n]
%o A063962 -- _Reinhard Zumkeller_, Apr 05 2012
%Y A063962 Cf. A055399, A001221.
%Y A063962 Cf. A027748, A063962.
%Y A063962 Zeros are at indices A008578.
%Y A063962 The divisors are listed by A161906 and add up to A097974.
%Y A063962 Dominates A333806 (the strictly inferior version).
%Y A063962 The superior version is A341591.
%Y A063962 The strictly superior version is A341642.
%Y A063962 A001221 counts prime divisors, with sum A001414.
%Y A063962 A033677 selects the smallest superior divisor.
%Y A063962 A038548 counts inferior divisors.
%Y A063962 A063538/A063539 have/lack a superior prime divisor.
%Y A063962 A161908 lists superior divisors.
%Y A063962 A207375 lists central divisors.
%Y A063962 A217581 selects the greatest inferior prime divisor.
%Y A063962 A341676 lists the unique superior prime divisors.
%Y A063962 - Inferior: A033676, A066839, A069288, A072499, A333749, A333750.
%Y A063962 - Superior: A051283, A059172, A070038, A072500, A116883, A341592, A341675.
%Y A063962 - Strictly Inferior: A056924, A060775, A070039, A333805, A341596, A341674.
%Y A063962 - Strictly Superior: A056924, A140271, A238535, A341594, A341595, A341673.
%Y A063962 Cf. A000005, A001248, A005117, A006530, A020639, A048098, A064052, A341643.
%K A063962 nonn
%O A063962 1,12
%A A063962 _Reinhard Zumkeller_, Sep 04 2001
%E A063962 Revised definition from _Emeric Deutsch_, Jan 31 2006