A341595 Number of strictly superior squarefree divisors of n.

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, 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, 2, 4, 1, 0, 1, 2, 1, 2, 2, 4, 1, 1, 0, 2, 1, 3, 2, 2, 2

Offset: 1

Author

Gus Wiseman, Feb 19 2021

Keywords

• nonn

Comments

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.

Examples

			The strictly superior squarefree divisors (columns) of selected n:
n = 1   2   6  30  60  210  420  630 1050 2310 4620 6930
    ----------------------------------------------------
    {}  2   3   6  10   15   21   30   35   55   70  105
            6  10  15   21   30   35   42   66   77  110
               15  30   30   35   42   70   70  105  154
               30       35   42   70  105   77  110  165
                        42   70  105  210  105  154  210
                        70  105  210       110  165  231
                       105  210            154  210  330
                       210                 165  231  385
                                           210  330  462
                                           231  385  770
                                           330  462 1155
                                           385  770 2310
                                           462 1155
                                           770 2310
                                          1155
                                          2310
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The inferior version is A333749.

The non-strict version is A341592.

The version for odd instead of squarefree divisors is A341594.

The strictly inferior version is A341596.

The version for prime instead of squarefree divisors is A341642.

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

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

A038548 counts superior (or inferior) divisors.

A056924 counts strictly superior (or strictly inferior) divisors.

A161908 lists superior divisors.

A207375 list central divisors.

A341673 lists strictly superior divisors.

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

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

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

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

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

Programs

Mathematica

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

PARI

a(n) = sumdiv(n, d, d^2 > n && issquarefree(d)); \\ Amiram Eldar, Nov 01 2024