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Smallest number requiring n steps to reach 0 or -1 when iterating the function: f(n)=lcd(n)-lpf(n), where lcd(n) is the largest common difference between consecutive divisors of n (ordered by size) and lpf(n) is the largest prime factor of n.
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%I #19 Aug 08 2020 14:36:12

%S 1,8,24,45,75,160,273,429,741,1001,1183,1547,2645,3553,4301,5423,

%T 10880,23465,33371,39109,49075,74011,98933,104371,107911,163489,

%U 263177,371591,409219,420727,631215,986537,1234459,1440299,2777775,3101857,3412783,3626797

%N Smallest number requiring n steps to reach 0 or -1 when iterating the function: f(n)=lcd(n)-lpf(n), where lcd(n) is the largest common difference between consecutive divisors of n (ordered by size) and lpf(n) is the largest prime factor of n.

%H Michael De Vlieger, <a href="/A074348/b074348.txt">Table of n, a(n) for n = 1..42</a>

%H Jason Earls, <a href="https://www.semanticscholar.org/paper/Smarandache-iterations-of-the-first-kind-on-and-Earls/3685dfcee58bf0d2e15a15198e4005ecbadc0c8a">Smarandache iterations of the first kind on functions involving divisors and prime factors</a>, in Smarandache Notions Journal (2004), Vol. 14.1, page 261.

%t With[{s = Array[Length@ NestWhileList[Function[n, Max@ Differences@ # - SelectFirst[Reverse@ #, PrimeQ] &@ Divisors[n]], #, # > 0 &] &, 10^5]}, Array[FirstPosition[s, #][[1]] &, Max@ s - 1, 2]] (* _Michael De Vlieger_, Mar 28 2018 *)

%Y Cf. A075661.

%K nonn

%O 1,2

%A _Jason Earls_, Sep 23 2002

%E a(28)-a(38) from _Michael De Vlieger_, Mar 28 2018