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Array read by rows in which row n lists the divisors of n that are >= sqrt(n).
38

%I #21 Mar 08 2021 09:19:30

%S 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,

%T 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,

%U 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

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

%C T(n,A038548(n)) = n. - _Reinhard Zumkeller_, Mar 08 2013

%C 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

%H Reinhard Zumkeller, <a href="/A161908/b161908.txt">Rows n = 1..1000 of triangle, flattened</a>

%e Array begins:

%e 1;

%e 2;

%e 3;

%e 2,4;

%e 5;

%e 3,6;

%e 7;

%e 4,8;

%e 3,9;

%e 5,10;

%e 11;

%e 4,6,12;

%e 13;

%e 7,14;

%e 5,15;

%e 4,8,16;

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

%o (Haskell)

%o a161908 n k = a161908_tabf !! (n-1) !! (k-1)

%o a161908_row n = a161908_tabf !! (n-1)

%o a161908_tabf = zipWith

%o (\x ds -> reverse $ map (div x) ds) [1..] a161906_tabf

%o -- _Reinhard Zumkeller_, Mar 08 2013

%Y Final terms are A000027.

%Y Initial terms are A033677.

%Y Row lengths are A038548 (number of superior divisors).

%Y Row sums are A070038 (sum of superior divisors).

%Y The inferior version is A161906.

%Y The prime terms are counted by A341591.

%Y The squarefree terms are counted by A341592.

%Y The prime-power terms are counted by A341593.

%Y The strictly superior version is A341673.

%Y The strictly inferior version is A341674.

%Y The odd terms are counted by A341675.

%Y A001221 counts prime divisors, with sum A001414.

%Y A056924 counts strictly superior (or strictly inferior divisors).

%Y A207375 lists central divisors.

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

%Y - Superior: A051283, A059172, A063538, A063539, A072500, A116882, A116883, A341592, 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. A000005, A000203, A001055, A001248, A006530, A020639, A050320, A161901.

%K easy,nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jun 27 2009

%E More terms from _Sean A. Irvine_, Nov 29 2010