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%I #11 May 14 2020 01:23:08
%S 1,2,4,12,6,3,9,18,36,144,48,16,80,20,10,5,15,30,60,180,90,45,225,75,
%T 25,50,100,300,150,450,900,3600,720,240,1200,400,2800,560,112,28,14,7,
%U 21,42,84,252,126,63,315,105,35,70,140,420,210,630,1260,5040,1008
%N Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the prime tower factorization of a(n+1) can be obtained from that of a(n) by adding or removing exactly one prime number.
%C The prime tower factorization of a number is defined in A182318.
%C For any n > 0, a(n+1) is either a multiple or a divisor of a(n).
%C For any prime number p, the sequence contains a multiple of p.
%H Rémy Sigrist, <a href="/A334766/b334766.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A334766/a334766.gp.txt">PARI program for A334766</a>
%F abs(A106490(a(n+1)) - A106490(a(n))) = 1.
%e The first terms, alongside their prime tower factorizations, are:
%e n a(n) Prime tower factorization of a(n)
%e -- ---- ---------------------------------
%e 1 1 1
%e 2 2 2
%e 3 4 2^2
%e 4 12 2^2 * 3
%e 5 6 2 * 3
%e 6 3 3
%e 7 9 3^2
%e 8 18 2 * 3^2
%e 9 36 2^2 * 3^2
%e 10 144 2^2^2 * 3^2
%e 11 48 2^2^2 * 3
%e 12 16 2^2^2
%e 13 80 2^2^2 * 5
%e 14 20 2^2 * 5
%e 15 10 2 * 5
%e 16 5 5
%o (PARI) See Links section.
%Y Cf. A106490, A182318, A298480.
%K nonn
%O 1,2
%A _Rémy Sigrist_, May 10 2020
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