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A379461 Irregular triangle read by rows in which row n lists the divisors m of n such that there is a divisor d of n with d < m < 2*d, or 0 if such divisors do not exist.

%I A379461 #39 Apr 26 2025 00:34:35
%S A379461 0,0,0,0,0,3,0,0,0,0,0,3,4,6,0,0,5,0,0,3,9,0,5,0,0,0,3,4,6,8,12,0,0,0,
%T A379461 7,0,3,5,6,10,15,0,0,0,0,7,3,4,6,9,12,18,0,0,0,5,8,10,0,3,7,21,0,0,5,
%U A379461 9,15,0,0,3,4,6,8,12,16,24,0,0,0,0,0,3,9,27,0
%N A379461 Irregular triangle read by rows in which row n lists the divisors m of n such that there is a divisor d of n with d < m < 2*d, or 0 if such divisors do not exist.
%C A379461 The number of positive terms in row n is A174903(n).
%C A379461 The indices of the rows that contain a zero give A174905.
%C A379461 The indices of the rows that contain positive integers give A005279.
%C A379461 The positive integers in the n-th row are the missing divisors of n in the n-th row of A379374.
%C A379461 The odd integers in the n-th row are the missing odd divisors of n in the n-th row of A379288.
%e A379461 Triangle begins:
%e A379461   0;
%e A379461   0;
%e A379461   0;
%e A379461   0;
%e A379461   0;
%e A379461   3;
%e A379461   0;
%e A379461   0;
%e A379461   0;
%e A379461   0;
%e A379461   0;
%e A379461   3, 4, 6;
%e A379461   0;
%e A379461   0;
%e A379461   5;
%e A379461   0;
%e A379461   0;
%e A379461   3, 9;
%e A379461   0;
%e A379461   5;
%e A379461   ...
%e A379461 From _Omar E. Pol_, Apr 19 2025: (Start)
%e A379461 For n = 12 there are three divisors m of 12 such that there is a divisor d of 12 with d < m < 2*d. Those divisors are 3, 4 and 6 as shown below:
%e A379461    d  <  m  <  2*d
%e A379461 --------------------
%e A379461    1            2
%e A379461    2     3      4
%e A379461    3     4      6
%e A379461    4     6      8
%e A379461    6           12
%e A379461   12           24
%e A379461 .
%e A379461 So the 12th row of the triangle is [3, 4, 6]. (End)
%t A379461 row[n_] := Module[{d = Partition[Divisors[n], 2, 1], e}, e = Select[d, #[[2]] < 2*#[[1]] &][[;; , 2]]; If[e == {}, {0}, e]]; Table[row[n], {n, 1, 55}] // Flatten (* _Amiram Eldar_, Dec 23 2024 *)
%Y A379461 Cf. A005279, A027750, A174903, A174905, A182469, A237271, A379288, A379374, A379379, A379384, A383209.
%K A379461 nonn,tabf
%O A379461 1,6
%A A379461 _Omar E. Pol_, Dec 23 2024
%E A379461 More terms from _Amiram Eldar_, Dec 23 2024
%E A379461 Name changed by _Omar E. Pol_, Feb 05 2025