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

1,4

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

Prog

(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

Crossrefs

Cf. A058972, A058971, A058977.

Cf. A000005.

Sequence in context: A367871 A087194 A331427 * A292879 A361027 A267131

Adjacent sequences: A058985 A058986 A058987 * A058989 A058990 A058991

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 17 2001

Extensions

More terms from Naohiro Nomoto, Jul 20 2001

Status

approved