A341673 Irregular triangle read by rows giving the strictly superior divisors of n.

2, 3, 4, 5, 3, 6, 7, 4, 8, 9, 5, 10, 11, 4, 6, 12, 13, 7, 14, 5, 15, 8, 16, 17, 6, 9, 18, 19, 5, 10, 20, 7, 21, 11, 22, 23, 6, 8, 12, 24, 25, 13, 26, 9, 27, 7, 14, 28, 29, 6, 10, 15, 30, 31, 8, 16, 32, 11, 33, 17, 34, 7, 35, 9, 12, 18, 36, 37, 19, 38, 13, 39

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..72.

Example

Row n = 18 lists the strictly superior divisors of 18, which are 6, 9, 18.
Triangle begins:
   1: {}
   2: 2
   3: 3
   4: 4
   5: 5
   6: 3,6
   7: 7
   8: 4,8
   9: 9
  10: 5,10
  11: 11
  12: 4,6,12
  13: 13
  14: 7,14
  15: 5,15
  16: 8,16
  17: 17
  18: 6,9,18
  19: 19
  20: 5,10,20

Mathematica

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

Crossrefs

Final terms in each row (except n = 1) are A000027.

Row lengths are A056924 (number of strictly superior divisors).

Initial terms in each row are A140271.

The weakly inferior version is A161906.

The weakly superior version is A161908.

Row sums are A238535.

The odd terms in each row are counted by A341594.

The squarefree terms in each row are counted by A341595.

The prime terms in each row are counted by A341642.

The strictly inferior version is A341674.

A001221 counts prime divisors, with sum A001414.

A038548 counts superior (or inferior) divisors.

A207375 list central divisors.

- Inferior: A033676, A063962, A066839, A069288, A217581, A333749, A333750.

- Superior: A033677, A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A341591, A341592, A341593, A341675, A341676.

- Strictly Inferior: A060775, A070039, A333805, A333806, A341596, A341677.

- Strictly Superior: A048098, A064052, A341643, A341644, A341646.

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

Sequence in context: A194551 A212644 A351285 * A278057 A366876 A330750

Adjacent sequences: A341670 A341671 A341672 * A341674 A341675 A341676

Keyword

nonn,tabf

Author

Gus Wiseman, Feb 22 2021

Status

approved