A101367 Perfect Abs. Real part of complex z such that Abs[(Total[Divisors[z]]-z)]=Abs[z].

5, 3, 19, 15, 29, 6, 74, 19, 111, 147, 185, 91, 197, 269, 122, 159, 72, 827, 1487, 2903, 968, 999, 702, 5803, 326, 2474, 7871

Offset: 0

Author

Ed Pegg Jr, Jan 13 2005

Keywords

• nonn

Comments

Having Perfect Abs is not as good as being Perfect. A complex number can also have Abundant Abs or Deficient Abs.

Examples

			The divisors for 269+92i are: 1, 2+I, 3+4i, 6+5i, 7+2i, 7+16i, 12+11i, 13+34i, 17+126i, 32+47i, 39+2i, 269+92i. The (sum - k) is 139+248i. Abs[139+248i] == Abs[269+92i]
		

Crossrefs

Cf. A101366, A102527, A102531, A102532, A102506, A102507.

Programs

Mathematica

Re[Sort[Select[Flatten[Table[a + b I, {a, 1, 500}, {b, 1, 500}]], Abs[Total[Divisors[ # ]] - # ] == Abs[ # ] &], Abs[ #1] < Abs[ #2] &]]

Extensions

Ten more terms from Hans Havermann, Jan 15 2005