A235671 - OEIS

%I #28 Jun 22 2015 13:14:50

%S 2,1,4,1,1,6,1,1,2,8,2,1,1,10,1,1,2,3,12,3,2,1,1,14,1,1,2,4,16,4,2,1,

%T 1,3,18,3,1,1,2,5,20,5,2,1,1,22,1,1,2,3,4,6,24,6,4,3,2,1,1,26,1,1,2,7,

%U 28,7,2,1,1,3,5,30,5,3,1,1,2,4,8,32,8,4,2,1

%N Triangle read by rows in which row n lists the proper divisors of n in increasing order, 2n, and the proper divisors of n in decreasing order.

%C Numerators of a sequence related to the symmetric structure of sigma, which arises from the structure of A237593. The structure in the first two octants is transformed in a structure in the 6th and 7th octants, which is similar to an isosceles triangle.

%C Denominators are in A007395.

%C Row sums give A074400.

%C Row lengths is A114003 (see the Jovovic's formula in A114003).

%H Harvey P. Dale, <a href="/A235671/b235671.txt">Table of n, a(n) for n = 1..1000</a>

%e The irregular triangle begins:

%e 2;

%e 1, 4, 1;

%e 1, 6, 1;

%e 1, 2, 8, 2, 1;

%e 1, 10, 1;

%e 1, 2, 3, 12, 3, 2, 1;

%e 1, 14, 1;

%e 1, 2, 4, 16, 4, 2, 1;

%e 1, 3, 18, 3, 1;

%e 1, 2, 5, 20, 5, 2, 1;

%e 1, 22, 1;

%e 1, 2, 3, 4, 6, 24, 6, 4, 3, 2, 1;

%e ...

%e Also:

%e 1;

%e 1/2, 2, 1/2;

%e 1/2, 3, 1/2;

%e 1/2, 1, 4, 1, 1/2;

%e 1/2, 5, 1/2;

%e 1/2, 1, 3/2, 6, 3/2, 1, 1/2;

%e 1/2, 7, 1/2;

%e 1/2, 1, 2, 8, 2, 1, 1/2;

%e 1/2, 3/2, 9, 3/2, 1/2;

%e 1/2, 1, 5/2, 10, 5/2, 1, 1/2;

%e 1/2, 11, 1/2;

%e 1/2, 1, 3/2, 2, 3, 12, 3, 2, 3/2, 1, 1/2;

%e ...

%t pd[n_]:=Module[{d=Most[Divisors[n]]},Flatten[Join[{d,{2n},Reverse[d]}]]]; Flatten[Array[pd,20]] (* _Harvey P. Dale_, Dec 22 2014 *)

%Y Cf. A000005, A001065, A027750, A056538, A074400, A000203, A114002, A114003, A236104, A237591, A237593, A237270, A233772, A233773.

%K nonn,frac,tabf

%O 1,1

%A _Omar E. Pol_, Jan 24 2014