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 A320641 Numbers that require a record number of iterations of the sum of odd divisors function (A000593) to reach 1. 0
 1, 2, 3, 5, 9, 17, 67, 193, 1069, 2137, 4273, 34183, 205097, 990361, 11884331, 38294881, 76589761, 574396453, 10339136153, 36177024721, 72354049441, 144708098881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It seems that 9 is the only composite term. a(2)-a(14) appear in De Koninck's book. a(2)-a(18) were calculated by Kim & Bayad. REFERENCES J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 54, entry 193. LINKS Daeyeoul Kim and Abdelmejid Bayad, Polygon Numbers Associated with the Sum of Odd Divisors Function, Experimental Mathematics, Vol. 26, No. 3 (2017), pp. 287-297. EXAMPLE 5 is in the sequence since iterating A000593 on 5, i.e. A000593(5) = 6, A000593(6) = 4, A000593(4) = 1, reaches 1 after 3 steps, more steps than for any number below 5. MATHEMATICA oddsigma[n_] := If[ n < 1, 0, Times @@ (If[ # < 3, 1, (#^(#2 + 1) - 1) / (# - 1)] & @@@ FactorInteger @ n)]; niter[n_] := Module[{c=0}, m=n; While[m>1, m = oddsigma[m]; c++]; c]; seq={}; sm=-1; Do[s=niter[n]; If[s>sm, AppendTo[seq, n]; sm=s], {n, 1, 10000}]; seq (* after Michael Somos at A000593 *) CROSSREFS Cf. A000593. Sequence in context: A014227 A334816 A064769 * A047021 A201359 A047031 Adjacent sequences:  A320638 A320639 A320640 * A320642 A320643 A320644 KEYWORD nonn,more AUTHOR Amiram Eldar, Oct 29 2018 EXTENSIONS a(19)-a(22) from Giovanni Resta, Oct 29 2018 STATUS approved

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Last modified September 27 10:28 EDT 2021. Contains 347689 sequences. (Running on oeis4.)