A161908 Array read by rows in which row n lists the divisors of n that are >= sqrt(n).

1, 2, 3, 2, 4, 5, 3, 6, 7, 4, 8, 3, 9, 5, 10, 11, 4, 6, 12, 13, 7, 14, 5, 15, 4, 8, 16, 17, 6, 9, 18, 19, 5, 10, 20, 7, 21, 11, 22, 23, 6, 8, 12, 24, 5, 25, 13, 26, 9, 27, 7, 14, 28, 29, 6, 10, 15, 30, 31, 8, 16, 32, 11, 33, 17, 34, 7, 35, 6, 9, 12, 18, 36, 37, 19, 38, 13, 39, 8, 10, 20, 40, 41, 7, 14, 21, 42, 43, 11, 22, 44, 9, 15, 45, 23, 46, 47, 8, 12, 16

Offset: 1

Author

Omar E. Pol, Jun 27 2009

Keywords

• easy
• nonn
• tabf

Comments

T(n,A038548(n)) = n. - Reinhard Zumkeller, Mar 08 2013

If we define a divisor d|n to be superior if d >= n/d, then superior divisors are counted by A038548 and listed by this sequence. - Gus Wiseman, Mar 08 2021

Examples

			Array begins:
1;
2;
3;
2,4;
5;
3,6;
7;
4,8;
3,9;
5,10;
11;
4,6,12;
13;
7,14;
5,15;
4,8,16;
		

Links

• Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened

Crossrefs

Final terms are A000027.

Initial terms are A033677.

Row lengths are A038548 (number of superior divisors).

Row sums are A070038 (sum of superior divisors).

The inferior version is A161906.

The prime terms are counted by A341591.

The squarefree terms are counted by A341592.

The prime-power terms are counted by A341593.

The strictly superior version is A341673.

The strictly inferior version is A341674.

The odd terms are counted by A341675.

A001221 counts prime divisors, with sum A001414.

A056924 counts strictly superior (or strictly inferior divisors).

A207375 lists central divisors.

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

- Superior: A051283, A059172, A063538, A063539, A072500, A116882, A116883, A341592, A341676.

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

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

Cf. A000005, A000203, A001055, A001248, A006530, A020639, A050320, A161901.

Programs

Haskell

a161908 n k = a161908_tabf !! (n-1) !! (k-1)
a161908_row n = a161908_tabf !! (n-1)
a161908_tabf = zipWith
               (\x ds -> reverse $ map (div x) ds) [1..] a161906_tabf
-- Reinhard Zumkeller, Mar 08 2013

Mathematica

Table[Select[Divisors[n],#>=Sqrt[n]&],{n,100}]//Flatten (* Harvey P. Dale, Jan 01 2021 *)

Extensions

More terms from Sean A. Irvine, Nov 29 2010