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%I #5 Mar 30 2012 17:22:58
%S 0,6,10,14,0,22,26,0,34,38,0,46,27,0,58,62,0,0,74,42,82,86,0,94,63,0,
%T 106,0,70,118,122,0,0,134,105,142,146,98,0,158,0,166,117,0,178,0,175,
%U 0,194,130,202,206,0,214,218,154,226,0,245,138,171,0,0,254
%N Greatest integer x such that x' = 2n+1, or 0 if there is no such x, where x' is the arithmetic derivative (A003415).
%C Bisection of A099303. In contrast to the sequence for even numbers, A102084, there appear to be an infinite number of zeros in this sequence (see A098700). The density of the zeros appears to be 1/3. Quite Often a(n) = 4n-2. For odd number 2n+1, an upper bound on the largest anti-derivative x appears to ((2n+1)/3)^(3/2).
%H T. D. Noe, <a href="/A189762/b189762.txt">Table of n, a(n) for n = 1..10000</a>
%t dn[0] = 0; dn[1] = 0; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; nn = 100; d = Array[dn, (nn/2)^2]; Table[pos = Position[d, n]; If[pos == {}, 0, pos[[-1, 1]]], {n, 3, nn, 2}]
%Y Cf. A003415, A099303, A102084 (another bisection of A099303).
%K nonn
%O 1,2
%A _T. D. Noe_, Apr 27 2011
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