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A343012 Lexicographically earliest sequence of distinct numbers whose partial products have mutually distinct exponents in their prime factorization (A130091).

%I A343012 #10 Apr 03 2021 08:42:57
%S A343012 1,2,4,3,6,5,8,9,10,7,12,15,14,11,16,18,20,21,22,13,24,25,27,28,30,32,
%T A343012 33,26,17,35,36,40,42,44,39,34,19,45,48,49,50,54,55,52,51,38,23,56,60,
%U A343012 63,64,66,65,68,57,46,29,70,72,75,77,78,80,81,84,85,76,69
%N A343012 Lexicographically earliest sequence of distinct numbers whose partial products have mutually distinct exponents in their prime factorization (A130091).
%C A343012 Is this sequence a permutation of the positive integers?
%H A343012 Amiram Eldar, <a href="/A343012/b343012.txt">Table of n, a(n) for n = 1..10000</a>
%e A343012 The first partial products are:
%e A343012 1
%e A343012 1 * 2 = 2 = 2^1
%e A343012 1 * 2 * 4 = 8 = 2^3
%e A343012 1 * 2 * 4 * 3 = 24 = 2^3 * 3^1
%e A343012 1 * 2 * 4 * 3 * 6 = 144 = 2^4 * 3^2
%t A343012 q[n_] := UnsameQ @@ FactorInteger[n][[;; , 2]]; seq = {1}; prod = 1; Do[k = 1; While[MemberQ[seq, k] || ! q[k*prod], k++]; AppendTo[seq, k]; prod *= k, {100}]; seq
%Y A343012 Cf. A130091, A343013.
%K A343012 nonn,look
%O A343012 1,2
%A A343012 _Amiram Eldar_, Apr 02 2021