A233773 -id:A233773 - cp's OEIS frontend

A233772 Triangle read by rows in which row n lists n together with the proper divisors of n multiplied by -1 in increasing order.

1, 2, -1, 3, -1, 4, -2, -1, 5, -1, 6, -3, -2, -1, 7, -1, 8, -4, -2, -1, 9, -3, -1, 10, -5, -2, -1, 11, -1, 12, -6, -4, -3, -2, -1, 13, -1, 14, -7, -2, -1, 15, -5, -3, -1, 16, -8, -4, -2, -1, 17, -1

Offset: 1

Omar E. Pol, Jan 03 2014

The same as A056538 but with all terms multiplied by -1 from the second column.

The sum of row n gives the deficiency of n.

			Written as an irregular triangle in which row n has length A000005(n) the sequence begins:
1;
2, -1;
3, -1;
4, -2, -1;
5, -1;
6, -3, -2, -1;
7, -1;
8, -4, -2, -1;
9, -3, -1;
10, -5, -2, -1;
11, -1;
12, -6, -4, -3, -2, -1;
...

Row sums give A033879.

Cf. A000005, A000203, A000396, A001065, A005100, A005101, A027750, A033880, A056538, A233773.

A235671 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.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Jan 24 2014

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.
Denominators are in A007395.
Row sums give A074400.
Row lengths is A114003 (see the Jovovic's formula in A114003).

			The irregular triangle begins:
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;
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;
...
Also:
1;
1/2, 2, 1/2;
1/2, 3, 1/2;
1/2, 1, 4, 1, 1/2;
1/2, 5, 1/2;
1/2, 1, 3/2, 6, 3/2, 1, 1/2;
1/2, 7, 1/2;
1/2, 1, 2, 8, 2, 1, 1/2;
1/2, 3/2, 9, 3/2, 1/2;
1/2, 1, 5/2, 10, 5/2, 1, 1/2;
1/2, 11, 1/2;
1/2, 1, 3/2, 2, 3, 12, 3, 2, 3/2, 1, 1/2;
...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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

cp's OEIS Frontend

A233772 Triangle read by rows in which row n lists n together with the proper divisors of n multiplied by -1 in increasing order.

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