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A353694 a(n) is the least multiple of n with mutually distinct exponents in its prime factorization (A130091).

%I A353694 #9 May 05 2022 08:59:06
%S A353694 1,2,3,4,5,12,7,8,9,20,11,12,13,28,45,16,17,18,19,20,63,44,23,24,25,
%T A353694 52,27,28,29,360,31,32,99,68,175,72,37,76,117,40,41,504,43,44,45,92,
%U A353694 47,48,49,50,153,52,53,54,275,56,171,116,59,360,61,124,63,64,325
%N A353694 a(n) is the least multiple of n with mutually distinct exponents in its prime factorization (A130091).
%H A353694 Amiram Eldar, <a href="/A353694/b353694.txt">Table of n, a(n) for n = 1..10000</a>
%F A353694 a(n) = n if and only if n is in A130091.
%F A353694 a(A130092(n)) > n.
%F A353694 a(n) = n * A353693(n).
%e A353694 a(2) = 2 since 2 = 2^1 has only one exponent (1) in its prime factorization.
%e A353694 a(6) = 12 since 6 = 2*3 has two equal exponents (1) in its prime factorization, and 2*6 = 12 = 2^2*3 has two distinct exponents (1 and 2).
%t A353694 a[n_] := Module[{k = n}, While[!UnsameQ @@ FactorInteger[k][[;; , 2]], k += n]; k]; Array[a, 100]
%Y A353694 Cf. A130091, A130092, A353693.
%K A353694 nonn
%O A353694 1,2
%A A353694 _Amiram Eldar_, May 04 2022