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%I #10 Feb 19 2018 14:46:06
%S 1,2,3,4,5,6,8,7,12,10,9,14,16,11,15,18,20,21,24,22,25,27,26,30,36,28,
%T 32,13,42,40,33,50,39,48,34,35,60,54,38,56,44,45,66,70,72,46,63,52,78,
%U 84,64,17,49,68,77,80,51,98,76,88,55,75,90,96,58,100,57
%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, if prime(k) divides a(n) then k divides a(n+1) (where prime(k) denotes the k-th prime).
%C In other words, for any n > 0, A290103(a(n)) divides a(n+1).
%C See also A299441 (where we consider only least prime factors) and A299442 (where we consider only greatest prime factors).
%H Rémy Sigrist, <a href="/A299440/b299440.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A299440/a299440.gp.txt">PARI program for A299440</a>
%e The first terms, alongside A290103(a(n)), are:
%e n a(n) A290103(a(n))
%e -- ---- -------------
%e 1 1 1
%e 2 2 1
%e 3 3 2
%e 4 4 1
%e 5 5 3
%e 6 6 2
%e 7 8 1
%e 8 7 4
%e 9 12 2
%e 10 10 3
%e 11 9 2
%e 12 14 4
%e 13 16 1
%e 14 11 5
%e 15 15 6
%e 16 18 2
%e 17 20 3
%e 18 21 4
%e 19 24 2
%e 20 22 5
%o (PARI) See Links section.
%Y Cf. A290103, A299441, A299442.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Feb 10 2018
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