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 A060775 #47 Dec 11 2024 23:40:57
%S A060775 1,1,1,1,1,2,1,2,1,2,1,3,1,2,3,2,1,3,1,4,3,2,1,4,1,2,3,4,1,5,1,4,3,2,
%T A060775 5,4,1,2,3,5,1,6,1,4,5,2,1,6,1,5,3,4,1,6,5,7,3,2,1,6,1,2,7,4,5,6,1,4,
%U A060775 3,7,1,8,1,2,5,4,7,6,1,8,3,2,1,7,5,2,3
%N A060775 The greatest divisor d|n such that d < n/d, with a(1) = 1.
%C A060775 Also: Largest divisor of n which is less than sqrt(n).
%C A060775 If n is not a square, then a(n) = A033676(n), else a(n) is strictly smaller than A033676(n) = sqrt(n) (except for a(1) = 1). - _M. F. Hasler_, Sep 20 2011
%C A060775 Record values occur for n = k * (k+1), for which a(n) = k. - _Franklin T. Adams-Watters_, May 01 2015
%C A060775 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 gives the greatest strictly inferior divisor, which may differ from the lower central divisor A033676. Central divisors are listed by A207375. - _Gus Wiseman_, Feb 28 2021
%H A060775 Alois P. Heinz, <a href="/A060775/b060775.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 2..1000 from Harry J. Smith)
%F A060775 a(n) = max { d: d|n and d < sqrt(n) or d = 1 }, where "|" means "divides". [Corrected by _M. F. Hasler_, Apr 03 2019]
%e A060775 n = 252, D = {1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252}, 18 divisors, the 9th is 14, so a(252) = 14.
%e A060775 From _Gus Wiseman_, Feb 28 2021: (Start)
%e A060775 The strictly inferior divisors of selected n:
%e A060775 n = 1 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240
%e A060775 -----------------------------------------------------------------
%e A060775 {} 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A060775 2 2 2 2 2 2 2 2 2 2 2 2 2 2
%e A060775 3 4 3 3 4 3 3 5 3 3 7 3 3
%e A060775 5 6 7 4 5 10 4 4 13 5 4
%e A060775 6 6 6 6 6 5
%e A060775 8 9 11 12 7 6
%e A060775 10 8
%e A060775 14 10
%e A060775 12
%e A060775 15
%e A060775 (End)
%p A060775 with(numtheory):
%p A060775 a:= n-> max(select(d-> is(d=1 or d<sqrt(n)), divisors(n))):
%p A060775 seq(a(n), n=1..100); # _Alois P. Heinz_, Jan 29 2018
%t A060775 Table[Part[Divisors[w], Floor[DivisorSigma[0, w]/2]], {w, 1, 256}]
%t A060775 Table[If[n==1,1,Max[Select[Divisors[n],#<n/#&]]],{n,100}] (* _Gus Wiseman_, Feb 28 2021 *)
%o A060775 (PARI) A060775(n)=if(n>1,divisors(n)[numdiv(n)\2],1) \\ _M. F. Hasler_, Sep 21 2011
%Y A060775 Cf. A033677, A000196, A000005, A000142, A027423, A055226, A060776, A060777, A002378.
%Y A060775 The weakly inferior version is A033676.
%Y A060775 Positions of first appearances are A180291.
%Y A060775 These are the row-maxima of A341674.
%Y A060775 A038548 counts superior (or inferior) divisors.
%Y A060775 A056924 counts strictly superior (or strictly inferior) divisors.
%Y A060775 A070039 adds up strictly inferior divisors.
%Y A060775 A207375 lists central divisors.
%Y A060775 A333805 counts strictly inferior odd divisors.
%Y A060775 A333806 counts strictly inferior prime divisors.
%Y A060775 A341596 counts strictly inferior squarefree divisors.
%Y A060775 A341677 counts strictly inferior prime-power divisors.
%Y A060775 - Inferior: A063962, A066839, A069288, A161906, A217581, A333749, A333750.
%Y A060775 - Superior: A051283, A059172, A063538, A063539, A070038, A161908, A341591.
%Y A060775 - Strictly Superior: A048098, A064052, A140271, A238535, A341642, A341673.
%Y A060775 Cf. A000203, A001248, A006530, A020639, A112798, A161901.
%K A060775 nonn,look
%O A060775 1,6
%A A060775 _Labos Elemer_, Apr 26 2001
%E A060775 a(1) = 1 added (to preserve the relation a(n) | n) by _Franklin T. Adams-Watters_, Jan 27 2018
%E A060775 Edited by _M. F. Hasler_, Apr 03 2019
%E A060775 Name changed by _Gus Wiseman_, Feb 28 2021 (was: Lower central (median) divisor of n, with a(1) = 1.)