For those who expressed interest in pursuing this further, here's a reference sent by Neil Sloane:

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Note the following sequence

%I A057641
%S A057641 0,0,1,0,4,0,7,2,7,5,13,0,17,9,12,8,23,5,27,8,21,20,34,1,33,25,
%T A057641 30,17,46,7,50,22,40,37,46,6,62,43,50,19,70,19,74,37,46,55,82,9,
%U A057641 79,46,70,47,95,32,83,38,81,74,107,2,112,81,76,56,102,45,125,70
%N A057641 Floor(H(n)+exp(H(n))*log(H(n))) - sigma(n), where H(n) = Sum_{k=1..n} 1/k and sigma(n) (A000203) is the sum of the divisors of n.
%C A057641 Showing this is nonnegative is equivalent to proving the Riemann hypothesis.
%H A057641 J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, Am. Math. Monthly 109 (#6, 2002), 534-543.
<http://arxiv.org/abs/math.NT/0008177>
%Y A057641 Cf. A057640, A000203, A076633.
%K A057641 nonn,nice,easy
%O A057641 1,5
%A A057641 njas, Oct 12 2000
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--Dan