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%I #14 May 20 2023 11:16:11
%S 1,2,3,5,7,4,6,11,9,13,10,15,14,17,8,19,21,25,12,22,23,18,35,26,33,20,
%T 27,49,39,30,29,28,34,55,31,16,45,38,42,65,51,50,77,24,37,57,63,44,75,
%U 46,91,36,70,85,41,52,66,40,69,43,95,54,105,121,98,125,78,119,99,60,58
%N Natural numbers sorted by the sum of square roots of prime factors.
%C Prime factors counted with multiplicity. - _Harvey P. Dale_, May 20 2023
%H J. Pohjonen, <a href="/A178595/b178595.txt">Table of n, a(n) for n=1..1000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F For n >= 1, Sum_{k=1..A001222(a(n))} sqrt(A027746(a(n),k)) < Sum_{k=1..A001222(a(n+1))} sqrt(A027746(a(n+1),k)). - _Peter Munn_, Aug 17 2022
%t SortBy[Table[{n,Total[N[Sqrt[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]]]},{n,150}],Last][[;;,1]] (* _Harvey P. Dale_, May 20 2023 *)
%Y Cf. A001222, A027746.
%Y Similarly defined sequences: A064364, A168521.
%K nonn
%O 1,2
%A _Joonas Pohjonen_, May 30 2010
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