%I #14 Apr 06 2015 06:57:34
%S 0,6,5,4,2,1,3,2,3,1,1,2,2,1,1,1,1,2,2,1,1,4,1,1,1,1,2,1,2,1,1,2,1,1,
%T 1,3,2,1,1,1,1,1,2,1,2,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,1,
%U 1,1,1,2,2,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1
%N a(n) is the number of iterations of the map x->sigma(x) when starting from n before arriving at a number with more than one ancestor, with a(1)=0 and where sigma is the sum of divisors.
%C That is, before arriving at a number x such that A054973(x) > 1.
%H G. L. Cohen and H. J. J. te Riele, <a href="http://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 93-100.
%e For n=2, the repeated map gives 2 -> 3 -> 4 -> 7 -> 8 -> 15 -> 24 where 24 is the first fork with sigma(15)=sigma(23)=24, so with 6 iterations starting from 2 we have a(2)=6, a(3)=5, a(4)=4, a(7)=3, a(8)=2, and a(15)=1.
%o (PARI) isfork(n) = {my(nba = 0); for (i=2, n-1, if (sigma(i) == n, nba++); if (nba > 1, return (1)););}
%o a(n) = {if (n==1, return (0)); my(nbit = 0); ok = 0; while (! ok, newn = sigma(n); nbit++; ok = isfork(newn); n = newn;); nbit;}
%Y Cf. A000203, A054973, A085790, A216200, A241954.
%K nonn
%O 1,2
%A _Michel Marcus_, Apr 03 2015