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A343505 a(n) is the least common multiple of the nonzero digits in factorial base expansion of 1/n.

%I A343505 #10 Apr 18 2021 10:21:16
%S A343505 1,1,2,2,4,1,6,3,6,2,60,2,120,3,3,6,1008,4,51480,1,4,30,6930,1,140,36,
%T A343505 60,20,16380,4,243374040,12,105,504,12,6,6126120,4680,168,3,314954640,
%U A343505 10,209969760,24,4,180180,1790848659600,6,924,6,660,1260,8303710615200
%N A343505 a(n) is the least common multiple of the nonzero digits in factorial base expansion of 1/n.
%C A343505 See the Wikipedia link for the construction method of 1/n in factorial base.
%H A343505 Rémy Sigrist, <a href="/A343505/b343505.txt">Table of n, a(n) for n = 1..5000</a>
%H A343505 Rémy Sigrist, <a href="/A343505/a343505.png">Colored logarithmic scatterplot of the sequence for n = 1..25000</a> (where the color is function of A052126(n))
%H A343505 Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system#Fractional_values">Factorial number system (Fractional values)</a>
%H A343505 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e A343505 The first terms, alongside 1/n in factorial base, are:
%e A343505   n   a(n)   1/n in factorial base
%e A343505   --  -----  -----------------------------------------
%e A343505    1      1  1
%e A343505    2      1  0.1
%e A343505    3      2  0.0 2
%e A343505    4      2  0.0 1 2
%e A343505    5      4  0.0 1 0 4
%e A343505    6      1  0.0 1
%e A343505    7      6  0.0 0 3 2 0 6
%e A343505    8      3  0.0 0 3
%e A343505    9      6  0.0 0 2 3 2
%e A343505   10      2  0.0 0 2 2
%e A343505   11     60  0.0 0 2 0 5 3 1 4 0 10
%e A343505   12      2  0.0 0 2
%e A343505   13    120  0.0 0 1 4 1 2 5 4 8 5 0 12
%e A343505   14      3  0.0 0 1 3 3 3
%e A343505   15      3  0.0 0 1 3
%e A343505   16      6  0.0 0 1 2 3
%e A343505   17   1008  0.0 0 1 2 0 2 3 6 8 9 0 9 2 7 0 16
%e A343505   18      4  0.0 0 1 1 4
%e A343505   19  51480  0.0 0 1 1 1 6 2 0 9 5 2 6 11 11 13 8 0 18
%e A343505   20      1  0.0 0 1 1
%o A343505 (PARI) a(n) = my (v=1, f=1/n); for (r=2, oo, if (f==0, return (v), floor(f), v=lcm(v, floor(f))); f=frac(f)*r)
%Y A343505 Cf. A052126, A294168, A343504.
%K A343505 nonn,look,base
%O A343505 1,3
%A A343505 _Rémy Sigrist_, Apr 17 2021