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A344181 Numbers such that repeated division by their largest factorial divisor (as long as such a divisor larger than one exists) eventually yields 1.

%I A344181 #30 May 22 2021 04:28:27
%S A344181 1,2,4,6,8,12,16,24,32,36,48,64,96,120,128,144,192,240,256,288,384,
%T A344181 480,512,576,720,768,864,960,1024,1152,1440,1536,1920,2048,2304,2880,
%U A344181 3072,3456,3840,4096,4320,4608,5040,5760,6144,6912,7680,8192,8640,9216,10080
%N A344181 Numbers such that repeated division by their largest factorial divisor (as long as such a divisor larger than one exists) eventually yields 1.
%C A344181 Numbers whose closure under map x -> A076934(x) contains 1.
%C A344181 Largest factorial divisor of n is A000142(A055874(n)).
%C A344181 These numbers could be called "greedy Jordan-Polya numbers", as their presence in A001013 can be determined by a simple greedy algorithm.
%H A344181 David A. Corneth, <a href="/A344181/b344181.txt">Table of n, a(n) for n = 1..10000</a>
%H A344181 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e A344181 12 = 2^2 * 3 is present, as the largest factorial that divides 12 is A000142(3) = 6, and then 12/6 = 2 is also divisible by a factorial, and then 2/A000142(2) = 1.
%t A344181 fctdiv[n_] := Module[{m = 1, k = 1}, While[Divisible[n, m], k++; m *= k]; m /= k; n/m]; Select[Range[10^4], FixedPoint[fctdiv, #] == 1 &] (* _Amiram Eldar_, May 22 2021 *)
%Y A344181 Cf. A000142, A055874, A076934.
%Y A344181 Positions of ones in A093411.
%Y A344181 Subsequence of A001013. A344179 gives the terms not present here.
%Y A344181 Cf. also A025487 (analogous sequence for primorials).
%K A344181 nonn
%O A344181 1,2
%A A344181 _Antti Karttunen_, May 18 2021