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A101366
Perfect Abs: Imaginary part of complex z such that Abs[(Total[Divisors[z]]-z)]=Abs[z].
4
3, 7, 8, 42, 48, 57, 33, 82, 78, 77, 83, 189, 154, 92, 321, 341, 549, 664, 106, 1034, 2929, 4072, 5049, 3037, 6957, 7097, 5051
OFFSET
0,1
COMMENTS
Having Perfect Abs is not as good as being Perfect. A complex number can also have Abundant Abs or Deficient Abs.
EXAMPLE
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]
The sequence of complex z's is: 5+3i, 3+7i, 19+8i, 15+42i, 6+57i, 29+48i, 19+82i, 74+33i, 111+78i, 147+77i, 185+83i, 91+189i, 197+154i, 269+92i, 122+321i, 159+341i, 72+549i, ...
MATHEMATICA
Im[Sort[Select[Flatten[Table[a + b I, {a, 1, 500}, {b, 1, 500}]], Abs[Total[Divisors[ # ]] - # ] == Abs[ # ] &], Abs[ #1] < Abs[ #2] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ed Pegg Jr, Jan 13 2005
EXTENSIONS
Ten more terms from Hans Havermann, Jan 15 2005
STATUS
approved