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A058972
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For a rational number p/q let f(p/q) = sum of aliquot divisors of p+q divided by number of divisors of p+q; sequence gives numbers n such that, starting at n/1 and iterating f, an integer is eventually reached.
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8
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3, 9, 15, 24, 25, 29, 33, 35, 50, 51, 55, 57, 59, 63, 73, 79, 80, 81, 85, 87, 89, 90, 95, 99, 105, 119, 120, 121, 128, 131, 139, 143, 145, 169, 177, 179, 181, 183, 193, 195, 201, 203, 204, 211, 215, 217, 218, 219, 221, 225, 227, 233, 247, 248, 255, 273, 275, 288
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Matthew M. Conroy, Home page (listed instead of email address)
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EXAMPLE
| f(9/1) = 8/4 = 2, an integer, so 9 is in the sequence; f(10/1) = 1/2 and f(1/2)=1/2, so 10 is not in the sequence.
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MATHEMATICA
| f[r_] := If[init == False && IntegerQ[r], r, init = False; p = Numerator[r]; q = Denominator[r]; d = Most[Divisors[p+q]]; Total[d]/(Length[d]+1)]; ok[n_] := IntegerQ[ init = True; FixedPoint[f, n/1]]; ok[1] = False; A058972 = Select[ Range[300], ok] (* From Jean-François Alcover, Dec 21 2011 *)
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CROSSREFS
| Cf. A058971, A058973.
Sequence in context: A029482 A174786 A139419 * A026222 A192720 A099989
Adjacent sequences: A058969 A058970 A058971 * A058973 A058974 A058975
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 14 2001
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EXTENSIONS
| Corrected and extended by Matthew M. Conroy, Apr 18 2001
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