A161906 Triangle read by rows in which row n lists the divisors of n that are <= sqrt(n).
1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 2, 4, 1, 1, 2, 3, 1, 1, 2, 4, 1, 3, 1, 2, 1, 1, 2, 3, 4, 1, 5, 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, 6, 1, 1, 2, 1, 3, 1, 2, 4, 5, 1, 1, 2, 3, 6, 1, 1, 2, 4, 1, 3, 5, 1, 2, 1, 1, 2, 3
Offset: 1
Examples
Triangle begins: 1....... 1; 2....... 1; 3....... 1; 4..... 1,2; 5....... 1; 6..... 1,2; 7....... 1; 8..... 1,2; 9..... 1,3; 10..... 1,2; 11....... 1; 12... 1,2,3; 13....... 1; 14..... 1,2; 15..... 1,3; 16... 1,2,4;
Links
- Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened
Crossrefs
Initial terms are A000012.
Final terms are A033676.
Row lengths are A038548 (number of inferior divisors).
Row sums are A066839 (sum of inferior divisors).
The prime terms are counted by A063962.
The odd terms are counted by A069288.
Row products are A072499.
Row LCMs are A072504.
The superior version is A161908.
The squarefree terms are counted by A333749.
The prime-power terms are counted by A333750.
The strictly superior version is A341673.
The strictly inferior version is A341674.
A056924 count strictly superior (or strictly inferior divisors).
A207375 lists central divisors.
- Inferior: A217581.
- Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A341591, A341592, A341593, A341675, A341676.
Programs
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Haskell
a161906 n k = a161906_tabf !! (n-1) !! (k-1) a161906_row n = a161906_tabf !! (n-1) a161906_tabf = zipWith (\m ds -> takeWhile ((<= m) . (^ 2)) ds) [1..] a027750_tabf' -- Reinhard Zumkeller, Jun 24 2015, Mar 08 2013 -
Mathematica
div[n_] := Select[Divisors[n], # <= Sqrt[n] &]; div /@ Range[48] // Flatten (* Amiram Eldar, Nov 13 2020 *)
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PARI
row(n) = select(x->(x<=sqrt(n)), divisors(n)); \\ Michel Marcus, Nov 13 2020
Extensions
More terms from Sean A. Irvine, Nov 29 2010
Comments