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A096335 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. 3

%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

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Last modified May 9 08:25 EDT 2021. Contains 343699 sequences. (Running on oeis4.)