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A161906 Triangle read by rows in which row n lists the divisors of n that are <= sqrt(n).

%I A161906 #34 Mar 08 2021 09:19:23
%S A161906 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,
%T A161906 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,
%U A161906 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
%N A161906 Triangle read by rows in which row n lists the divisors of n that are <= sqrt(n).
%C A161906 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
%H A161906 Reinhard Zumkeller, <a href="/A161906/b161906.txt">Rows n = 1..1000 of triangle, flattened</a>
%e A161906 Triangle begins:
%e A161906    1....... 1;
%e A161906    2....... 1;
%e A161906    3....... 1;
%e A161906    4..... 1,2;
%e A161906    5....... 1;
%e A161906    6..... 1,2;
%e A161906    7....... 1;
%e A161906    8..... 1,2;
%e A161906    9..... 1,3;
%e A161906   10..... 1,2;
%e A161906   11....... 1;
%e A161906   12... 1,2,3;
%e A161906   13....... 1;
%e A161906   14..... 1,2;
%e A161906   15..... 1,3;
%e A161906   16... 1,2,4;
%t A161906 div[n_] := Select[Divisors[n], # <= Sqrt[n] &]; div /@ Range[48] // Flatten (* _Amiram Eldar_, Nov 13 2020 *)
%o A161906 (Haskell)
%o A161906 a161906 n k = a161906_tabf !! (n-1) !! (k-1)
%o A161906 a161906_row n = a161906_tabf !! (n-1)
%o A161906 a161906_tabf = zipWith (\m ds -> takeWhile ((<= m) . (^ 2)) ds)
%o A161906                        [1..] a027750_tabf'
%o A161906 -- _Reinhard Zumkeller_, Jun 24 2015, Mar 08 2013
%o A161906 (PARI) row(n) = select(x->(x<=sqrt(n)), divisors(n)); \\ _Michel Marcus_, Nov 13 2020
%Y A161906 Initial terms are A000012.
%Y A161906 Final terms are A033676.
%Y A161906 Row lengths are A038548 (number of inferior divisors).
%Y A161906 Row sums are A066839 (sum of inferior divisors).
%Y A161906 The prime terms are counted by A063962.
%Y A161906 The odd terms are counted by A069288.
%Y A161906 Row products are A072499.
%Y A161906 Row LCMs are A072504.
%Y A161906 The superior version is A161908.
%Y A161906 The squarefree terms are counted by A333749.
%Y A161906 The prime-power terms are counted by A333750.
%Y A161906 The strictly superior version is A341673.
%Y A161906 The strictly inferior version is A341674.
%Y A161906 A001221 counts prime divisors, with sum A001414.
%Y A161906 A000005 counts divisors, listed by A027750 with sum A000203.
%Y A161906 A056924 count strictly superior (or strictly inferior divisors).
%Y A161906 A207375 lists central divisors.
%Y A161906 - Inferior: A217581.
%Y A161906 - Superior: A033677, A051283, A059172, A063538, A063539, A070038, A116882, A116883, A341591, A341592, A341593, A341675, A341676.
%Y A161906 - Strictly Inferior: A060775, A070039, A333805, A333806, A341596, A341677.
%Y A161906 - Strictly Superior: A048098, A064052, A140271, A238535, A341594, A341595, A341642, A341643, A341644, A341645, A341646.
%Y A161906 Cf. A000196, A001055, A001248, A006530, A020639, A050320, A068101, A161901.
%K A161906 easy,nonn,tabf
%O A161906 1,5
%A A161906 _Omar E. Pol_, Jun 27 2009
%E A161906 More terms from _Sean A. Irvine_, Nov 29 2010