A233773 Triangle read by rows in which row n lists the proper divisors of n together with -n.

-1, 1, -2, 1, -3, 1, 2, -4, 1, -5, 1, 2, 3, -6, 1, -7, 1, 2, 4, -8, 1, 3, -9, 1, 2, 5, -10, 1, -11, 1, 2, 3, 4, 6, -12, 1, -13, 1, 2, 7, -14, 1, 3, 5, -15, 1, 2, 4, 8, -16, 1, -17, 1, 2, 3, 6, 9, -18, 1, -19, 1, 2, 4, 5, 10, -20, 1, 3, 7, -21, 1, 2, 11, -22, 1, -23

Offset: 1

Author

Omar E. Pol, Dec 31 2013

Keywords

• sign
• tabf

Comments

The same as A027750 but with the last term of every row multiplied by -1.

The sum of row n gives the abundance of n.

Examples

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

Links

• Eric Weisstein's World of Mathematics, Abundance
• Eric Weisstein's World of Mathematics, Quasiperfect Number

Crossrefs

Row sums give A033880.

Cf. A000005, A000203, A000396, A001065, A005100, A005101, A027750, A027751, A033879.

Cf. A137510, A163870.

Programs

Mathematica

Flatten[Table[Join[{Most[Divisors[n]]},{-n}],{n,30}]] (* Harvey P. Dale, Feb 20 2016 *)