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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

Table of n, a(n) for n=1..22.

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.)