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Search: id:A101366
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| A101366 |
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Perfect Abs: Imaginary part of complex z such that Abs[(Total[Divisors[z]]-z)]=Abs[z]. |
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+0
5
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Having Perfect Abs isn't as good as being Perfect. A complex number can also have Abundant Abs or Deficient Abs.
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EXAMPLE
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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, ...
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MAPLE
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Im[Sort[Select[Flatten[Table[a + b I, {a, 1, 500}, {b, 1, 500}]], Abs[Total[Divisors[ # ]] - # ] == Abs[ # ] &], Abs[ #1] < Abs[ #2] &]
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CROSSREFS
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Cf. A101367, A102526, A102531, A102532.
Adjacent sequences: A101363 A101364 A101365 this_sequence A101367 A101368 A101369
Sequence in context: A037208 A102007 A105756 this_sequence A090458 A131712 A072845
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KEYWORD
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nonn
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AUTHOR
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Ed Pegg Jr (ed(AT)mathpuzzle.com), Jan 13 2005
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EXTENSIONS
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Ten more terms from Hans Havermann (pxp(AT)rogers.com), Jan 15 2005
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