A341674 Irregular triangle read by rows giving the strictly inferior divisors of n.

1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 1, 3, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 3, 1, 2, 4, 1, 1, 2, 3, 5, 1, 1, 2, 4, 1, 3, 1, 2, 1, 5, 1, 2, 3, 4, 1, 1, 2, 1, 3, 1, 2, 4, 5, 1, 1, 2, 3, 6, 1, 1, 2, 4, 1, 3

Offset

1,6

Comments

We define a divisor d|n to be strictly inferior if d < n/d. The number of strictly inferior divisors of n is A056924(n).

Links

Table of n, a(n) for n=1..87.

Example

Triangle begins:
     1: {}        16: 1,2        31: 1
     2: 1         17: 1          32: 1,2,4
     3: 1         18: 1,2,3      33: 1,3
     4: 1         19: 1          34: 1,2
     5: 1         20: 1,2,4      35: 1,5
     6: 1,2       21: 1,3        36: 1,2,3,4
     7: 1         22: 1,2        37: 1
     8: 1,2       23: 1          38: 1,2
     9: 1         24: 1,2,3,4    39: 1,3
    10: 1,2       25: 1          40: 1,2,4,5
    11: 1         26: 1,2        41: 1
    12: 1,2,3     27: 1,3        42: 1,2,3,6
    13: 1         28: 1,2,4      43: 1
    14: 1,2       29: 1          44: 1,2,4
    15: 1,3       30: 1,2,3,5    45: 1,3,5

Mathematica

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

Crossrefs

Initial terms are A000012.

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

Final terms are A060775.

Row sums are A070039 (sum of strictly inferior divisors).

The weakly inferior version is A161906.

The weakly superior version is A161908.

The odd terms are counted by A333805.

The prime terms are counted by A333806.

The squarefree terms are counted by A341596.

The strictly superior version is A341673.

The prime-power terms are counted by A341677.

A001221 counts prime divisors, with sum A001414.

A001222 counts prime-power divisors.

A005117 lists squarefree numbers.

A038548 counts superior (or inferior) divisors.

A207375 lists central divisors.

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

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

- Strictly Superior: A048098, A064052, A140271, A238535, A341594, A341595, A341642, A341643, A341644, A341645, A341646.

Cf. A000005, A000203, A001055, A001248, A006530, A020639, A050320.

Sequence in context: A161111 A161046 A330556 * A363922 A230404 A082647

Adjacent sequences: A341671 A341672 A341673 * A341675 A341676 A341677

Keyword

nonn,tabf

Author

Gus Wiseman, Feb 23 2021

Status

approved