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).
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.
A001222 counts prime-power divisors.
A005117 lists squarefree numbers.
A038548 counts superior (or inferior) divisors.
A207375 lists central divisors.
- Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A341591, A341592, A341593, A341675, A341676.
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Feb 23 2021
STATUS
approved