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A375038 Irregular triangle read by rows T(n,k), n >= 2, k >= 1, in which row n lists the nonmiddle divisors of n.

%I A375038 #42 Aug 17 2024 23:11:20
%S A375038 2,1,3,1,4,1,5,1,6,1,7,1,4,8,1,9,1,2,5,10,1,11,1,2,6,12,1,13,1,2,7,14,
%T A375038 1,15,1,2,8,16,1,17,1,2,6,9,18,1,19,1,2,10,20,1,3,7,21,1,2,11,22,1,23,
%U A375038 1,2,3,8,12,24,1,25,1,2,13,26,1,3,9,27,1,2,14,28
%N A375038 Irregular triangle read by rows T(n,k), n >= 2, k >= 1, in which row n lists the nonmiddle divisors of n.
%C A375038 Except the 1, all positive integers have nonmiddle divisors.
%C A375038 The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).
%H A375038 Amiram Eldar, <a href="/A375038/b375038.txt">Table of n, a(n) for n = 2..6375</a> (rows for n = 2..1000, flattened)
%e A375038 Triangle begins starting in row n = 2:
%e A375038   2;
%e A375038   1, 3;
%e A375038   1, 4;
%e A375038   1, 5;
%e A375038   1, 6;
%e A375038   1, 7;
%e A375038   1, 4, 8;
%e A375038   1, 9;
%e A375038   1, 2, 5, 10;
%e A375038   1, 11;
%e A375038   1, 2, 6, 12;
%e A375038   ...
%e A375038 For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors are [3, 4], so the nonmiddle divisors are [1, 2, 6, 12], the same as the row n = 12 of the triangle.
%t A375038 row[n_] := Select[Divisors[n], !(Sqrt[n/2] <= # < Sqrt[2*n]) &]; Table[row[n], {n, 2, 28}] // Flatten (* _Amiram Eldar_, Jul 29 2024 *)
%Y A375038 Nonzero terms of A375037.
%Y A375038 The sum of row n is A302433(n).
%Y A375038 The number of terms in row n is A067743(n).
%Y A375038 Column 1 gives A054977.
%Y A375038 Cf. A027750, A067742, A071090, A299761, A303297.
%K A375038 nonn,tabf,easy,look
%O A375038 2,1
%A A375038 _Omar E. Pol_, Jul 28 2024