The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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
 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, 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, 2, 3, 2, 3, 1, 2, 0, 25, 0, 2, 0, 2, 1, 1, 1, 1, 0, 1, 39, 24, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). The graph looks like a forest of stalks. The tops of the stalks form A036434. - N. J. A. Sloane, Jan 17 2013 REFERENCES Claudia Spiro, Problem proposed at West Coast Number Theory Meeting, 1977. - From N. J. A. Sloane, Jan 11 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..11000 T. D. Noe, Logarithmic plot of 10^6 terms EXAMPLE a(6)=3 because the trajectory for 1 (sequence A064491) starts 1->2->4->7->9->12->18->24->32->38->42... and the trajectory for 6 starts 6->10->14->18->24->32->38->42->50->56... so the sequence beginning with 6 joins A064491 after 3 steps. MATHEMATICA 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 *) CROSSREFS Cf. A000005, A036434, A064491, A096335. Sequence in context: A328376 A141097 A278045 * A191910 A129503 A225682 Adjacent sequences: A096332 A096333 A096334 * A096336 A096337 A096338 KEYWORD nonn AUTHOR Jason Earls, Jun 28 2004 EXTENSIONS Escape clause added to definition by N. J. A. Sloane, Nov 09 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 14:41 EST 2022. Contains 358405 sequences. (Running on oeis4.)