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A058972 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. 8
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; text; internal format)
OFFSET

1,1

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

P. Schogt, The Wild Number Problem: math or fiction?, arXiv preprint arXiv:1211.6583, 2012. - From N. J. A. Sloane, Jan 03 2013

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.

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] (* Jean-Fran├žois Alcover, Dec 21 2011 *)

PROG

(Haskell)

import Data.Ratio ((%), numerator, denominator)

a058972 n = a058972_list !! (n-1)

a058972_list = map numerator $ filter ((f [])) [1..] where

   f ys q = denominator y == 1 || not (y `elem` ys) && f (y : ys) y

            where y = a001065 q' % a000005 q'

                  q' = numerator q + denominator q

-- Reinhard Zumkeller, Jun 15 2013

CROSSREFS

Cf. A058971, A058973.

Cf. A001065, A000005.

Sequence in context: A246298 A139419 A323031 * A026222 A192720 A099989

Adjacent sequences:  A058969 A058970 A058971 * A058973 A058974 A058975

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Jan 14 2001

EXTENSIONS

Corrected and extended by Matthew Conroy, Apr 18 2001

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)