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Search: id:A101367
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| A101367 |
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Perfect Abs. Real part of complex z such that Abs[(Total[Divisors[z]]-z)]=Abs[z]. |
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+0
5
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| 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
(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 is not 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]
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MATHEMATICA
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Re[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. A101366, A102527, A102531, A102532, A102506, A102507.
Sequence in context: A075453 A073845 A092525 this_sequence A049457 A061037 A070262
Adjacent sequences: A101364 A101365 A101366 this_sequence A101368 A101369 A101370
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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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