A058988 For a rational number p/q let f(p/q) = p*q divided by number of divisors of p+q; a(n) is obtained by iterating f, starting at n/1, until an integer is reached, or if no integer is ever reached then a(n) = 0.

1, 1, 1, 2, 30, 3, 14, 12, 18, 5, 33, 6, 26, 21, 3, 8, 51, 9, 38, 5, 28, 11, 92, 8, 50, 0, 9, 14, 116, 15, 93, 8, 66, 17, 105, 18, 74, 0, 156, 20, 492, 21, 86, 22, 60, 23, 0, 16, 147, 0, 17, 26, 212, 27, 330, 14, 114, 29, 354, 30, 61, 186, 9, 16, 260, 33, 201, 17, 138, 35, 426

Offset: 1

Author

N. J. A. Sloane, Jan 17 2001

Keywords

• nonn
• easy

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 [math.HO], 2012. - From _N. J. A. Sloane_, Jan 03 2013

Crossrefs

Cf. A058972, A058971, A058977.

Cf. A000005.

Programs

Haskell

import Data.Ratio ((%), numerator, denominator)
a058988 n = numerator $ fst $
  until ((== 1) . denominator . fst) f $ f (fromIntegral n, []) where
  f (x, ys) = if y `elem` ys then (0, []) else (y, y:ys) where
   y = numerator x * denominator x % a000005 (numerator x + denominator x)
-- Reinhard Zumkeller, Aug 29 2014

PARI

f2(p,q) = p*q/numdiv(p+q);
f1(r) = f2(numerator(r), denominator(r));
loop(list) = {my(v=Vecrev(list)); for (i=2, #v, if (v[i] == v[1], return(1)););}
a(n) = {my(ok=0, m=f2(n,1), list=List()); while(denominator(m) != 1, m = f1(m); listput(list, m); if (loop(list), return (0));); return(m);} \\ Michel Marcus, Feb 09 2022

Extensions

More terms from Naohiro Nomoto, Jul 20 2001