

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
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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. 287297.


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



