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A161906
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Triangle read by rows in which row n lists the divisors of n that are <= sqrt(n).
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46
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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
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OFFSET
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1,5
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COMMENTS
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If we define a divisor d|n to be inferior if d <= n/d, then inferior divisors are counted by A038548 and listed by this sequence. - Gus Wiseman, Mar 08 2021
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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div[n_] := Select[Divisors[n], # <= Sqrt[n] &]; div /@ Range[48] // Flatten (* Amiram Eldar, Nov 13 2020 *)
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PROG
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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'
(PARI) row(n) = select(x->(x<=sqrt(n)), divisors(n)); \\ Michel Marcus, Nov 13 2020
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CROSSREFS
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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.
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).
- 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.
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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