A341594 Number of strictly superior odd divisors of n.

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

Offset: 1

Author

Gus Wiseman, Feb 23 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 a(n) divisors for n = 3, 15, 45, 105, 315, 405, 945, 1575, 1890:
  3  5   9   15   21   27   35   45    45
     15  15  21   35   45   45   63    63
         45  35   45   81   63   75    105
             105  63   135  105  105   135
                  105  405  135  175   189
                  315       189  225   315
                            315  315   945
                            945  525
                                 1575
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

On odd indices, equals A056924 (number of strictly superior divisors).

The inferior version is A069288.

Positions of zeros are A116882.

Positions of nonzero terms are A116883.

The strictly inferior version is A333805.

The version for squarefree instead of odd divisors is A341595.

The version for prime instead of odd divisors is A341642.

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

The superior version is A341675.

A033676 selects the greatest inferior divisor.

A033677 selects the smallest superior divisor.

A038548 counts superior (or inferior) divisors.

A140271 selects the smallest strictly superior divisor.

A207375 lists central divisors.

A341673 lists strictly superior divisors.

- Inferior: A063962, A066839, A161906, A217581, A333749, A333750.

- Superior: A051283, A059172, A063538, A063539, A070038, A161908, A341591, A341592, A341593, A341676.

- Strictly Inferior: A060775, A070039, A333806, A341596, A341674.

- Strictly Superior: A048098, A064052, A238535, A341643, A341645, A341646.

Cf. A000005, A000203, A000265, A001222, A001248, A005408, A006530, A020639, A027193, A058695, A340101.

Programs

Mathematica

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

PARI

A341594(n) = sumdiv(n,d,(d%2)*(d>(n/d))); \\ Antti Karttunen, Feb 23 2021