%I #14 Nov 01 2024 05:15:10

%S 0,1,1,0,1,2,1,0,0,2,1,1,1,2,2,0,1,1,1,2,2,2,1,1,0,2,0,2,1,4,1,0,2,2,

%T 2,0,1,2,2,1,1,4,1,2,1,2,1,0,0,1,2,2,1,0,2,1,2,2,1,3,1,2,1,0,2,4,1,2,

%U 2,4,1,0,1,2,1,2,2,4,1,1,0,2,1,3,2,2,2

%N Number of strictly superior squarefree divisors of n.

%C We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.

%H Amiram Eldar, <a href="/A341595/b341595.txt">Table of n, a(n) for n = 1..10000</a>

%e The strictly superior squarefree divisors (columns) of selected n:

%e n = 1 2 6 30 60 210 420 630 1050 2310 4620 6930

%e ----------------------------------------------------

%e {} 2 3 6 10 15 21 30 35 55 70 105

%e 6 10 15 21 30 35 42 66 77 110

%e 15 30 30 35 42 70 70 105 154

%e 30 35 42 70 105 77 110 165

%e 42 70 105 210 105 154 210

%e 70 105 210 110 165 231

%e 105 210 154 210 330

%e 210 165 231 385

%e 210 330 462

%e 231 385 770

%e 330 462 1155

%e 385 770 2310

%e 462 1155

%e 770 2310

%e 1155

%e 2310

%t Table[Length[Select[Divisors[n],SquareFreeQ[#]&&#>n/#&]],{n,100}]

%o (PARI) a(n) = sumdiv(n, d, d^2 > n && issquarefree(d)); \\ _Amiram Eldar_, Nov 01 2024

%Y The inferior version is A333749.

%Y The non-strict version is A341592.

%Y The version for odd instead of squarefree divisors is A341594.

%Y The strictly inferior version is A341596.

%Y The version for prime instead of squarefree divisors is A341642.

%Y The version for prime-power instead of squarefree divisors is A341644.

%Y Positions of 0's are A341645, with complement A341646.

%Y A038548 counts superior (or inferior) divisors.

%Y A056924 counts strictly superior (or strictly inferior) divisors.

%Y A161908 lists superior divisors.

%Y A207375 list central divisors.

%Y A341673 lists strictly superior divisors.

%Y - Inferior: A033676, A063962, A066839, A069288, A161906, A217581, A333750.

%Y - Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A341593, A341675, A341676.

%Y - Strictly Inferior: A060775, A333805, A333806, A341674.

%Y - Strictly Superior: A048098, A064052 A140271, A238535, A341591, A341643.

%Y Cf. A000005, A000203, A001221, A001222, A001248, A006530, A020639, A112798.

%K nonn

%O 1,6

%A _Gus Wiseman_, Feb 19 2021