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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
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 * A365640 A047021 A201359
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Oct 29 2018
EXTENSIONS
a(19)-a(22) from Giovanni Resta, Oct 29 2018
STATUS
approved