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A083347 Numbers k such that Sum(e/p: k=Product(p^e)) < 1.

%I A083347 #38 Feb 21 2024 01:45:27
%S A083347 1,2,3,5,6,7,9,10,11,13,14,15,17,19,21,22,23,25,26,29,31,33,34,35,37,
%T A083347 38,39,41,42,43,45,46,47,49,50,51,53,55,57,58,59,61,62,63,65,66,67,69,
%U A083347 70,71,73,74,75,77,78,79,82,83,85,86,87,89,91,93,94,95,97,98,99,101,102
%N A083347 Numbers k such that Sum(e/p: k=Product(p^e)) < 1.
%C A083347 Numbers k whose arithmetic derivative (A003415) k' < k. - _T. D. Noe_, Apr 24 2011
%H A083347 T. D. Noe, <a href="/A083347/b083347.txt">Table of n, a(n) for n = 1..1000</a>
%F A083347 A083345(a(n)) < A083346(a(n));
%F A083347 A083345(A051674(n)) = A083346(A051674(n));
%F A083347 A083345(A083348(n)) > A083346(A083348(n)).
%F A083347 A168036(a(n)) < 0. - _Reinhard Zumkeller_, May 22 2015
%t A083347 Select[Range@ 102, If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger@ Abs@ #]] < # &] (* _Michael De Vlieger_, Feb 02 2019 *)
%o A083347 (Haskell)
%o A083347 a083347 n = a083347_list !! (n-1)
%o A083347 a083347_list = filter ((< 0) . a168036) [1..]
%o A083347 -- _Reinhard Zumkeller_, May 22 2015, May 10 2011
%Y A083347 Cf. A003415, A072873, A051674, A083348.
%Y A083347 Cf. A168036.
%K A083347 nonn
%O A083347 1,2
%A A083347 _Reinhard Zumkeller_, Apr 25 2003