%I
%S 0,0,2,0,1,3,0,1,0,2,8,0,7,1,6,5,6,0,5,3,4,3,4,0,3,2,13,2,13,1,12,0,
%T 11,1,10,8,10,0,9,7,9,0,8,1,7,1,8,6,7,0,6,6,6,5,5,0,4,5,4,26,3,4,2,0,
%U 2,3,2,3,1,2,0,25,0,2,0,2,1,1,1,1,0,1,39,24,38
%N Number of iterations of n > n + tau(n) needed for the trajectory of n to join the trajectory of A064491, or 1 if the two trajectories never merge.
%C Conjecture: For any positive integer starting value n, iterations of n > n + tau(n) will eventually join A064491 (verified for all n up to 50000).
%C The graph looks like a forest of stalks. The tops of the stalks form A036434.  _N. J. A. Sloane_, Jan 17 2013
%D Claudia Spiro, Problem proposed at West Coast Number Theory Meeting, 1977.  From _N. J. A. Sloane_, Jan 11 2013
%H T. D. Noe, <a href="/A096335/b096335.txt">Table of n, a(n) for n = 1..11000</a>
%H T. D. Noe, <a href="/A096335/a096335.gif">Logarithmic plot of 10^6 terms</a>
%e a(6)=3 because the trajectory for 1 (sequence A064491) starts
%e 1>2>4>7>9>12>18>24>32>38>42...
%e and the trajectory for 6 starts
%e 6>10>14>18>24>32>38>42>50>56...
%e so the sequence beginning with 6 joins A064491 after 3 steps.
%t s = 1; t = Join[{s}, Table[s = s + DivisorSigma[0, s], {n, 2, 1000}]]; mx = Max[t]; Table[r = n; gen = 0; While[r < mx && ! MemberQ[t, r], gen++; r = r + DivisorSigma[0, r]]; If[r >= mx, gen = 1]; gen, {n, 100}] (* _T. D. Noe_, Jan 13 2013 *)
%Y Cf. A000005, A036434, A064491, A096335.
%K nonn
%O 1,3
%A _Jason Earls_, Jun 28 2004
%E Escape clause added to definition by _N. J. A. Sloane_, Nov 09 2020
