cp's OEIS Frontend

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.

%I A058988 #18 Feb 09 2022 09:04:34
%S A058988 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,
%T A058988 14,116,15,93,8,66,17,105,18,74,0,156,20,492,21,86,22,60,23,0,16,147,
%U A058988 0,17,26,212,27,330,14,114,29,354,30,61,186,9,16,260,33,201,17,138,35,426
%N 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.
%H A058988 Reinhard Zumkeller, <a href="/A058988/b058988.txt">Table of n, a(n) for n = 1..10000</a>
%H A058988 P. Schogt, <a href="http://arxiv.org/abs/1211.6583">The Wild Number Problem: math or fiction?</a>, arXiv preprint arXiv:1211.6583 [math.HO], 2012. - From _N. J. A. Sloane_, Jan 03 2013
%o A058988 (Haskell)
%o A058988 import Data.Ratio ((%), numerator, denominator)
%o A058988 a058988 n = numerator $ fst $
%o A058988   until ((== 1) . denominator . fst) f $ f (fromIntegral n, []) where
%o A058988   f (x, ys) = if y `elem` ys then (0, []) else (y, y:ys) where
%o A058988    y = numerator x * denominator x % a000005 (numerator x + denominator x)
%o A058988 -- _Reinhard Zumkeller_, Aug 29 2014
%o A058988 (PARI) f2(p,q) = p*q/numdiv(p+q);
%o A058988 f1(r) = f2(numerator(r), denominator(r));
%o A058988 loop(list) = {my(v=Vecrev(list)); for (i=2, #v, if (v[i] == v[1], return(1)););}
%o A058988 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
%Y A058988 Cf. A058972, A058971, A058977.
%Y A058988 Cf. A000005.
%K A058988 nonn,easy
%O A058988 1,4
%A A058988 _N. J. A. Sloane_, Jan 17 2001
%E A058988 More terms from _Naohiro Nomoto_, Jul 20 2001