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