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%I #12 Aug 31 2018 21:17:26
%S 0,1,2,5,7,4,173,587,1481,1859,20701,18391,241393,275713,148367,
%T 548423,2342059,241321,41436061,19263077,40604659,43779103,1009564739,
%U 1907583043,9002492327,9603126977,27322095131,25887926681,752184042199
%N Numerators of the difference between the squarefree totient analogs of the harmonic numbers and the harmonic numbers: F_n-H_n.
%C F_n-H_n approaches a constant, 'kappa', conjectured to be equivalent to the difference of B_3-gamma, where B_3 is Mertens' 3rd constant and gamma is Euler's constant.
%H G. C. Greubel, <a href="/A138320/b138320.txt">Table of n, a(n) for n = 1..1000</a>
%H Dick Boland, <a href="http://www.imathination.org/kappa/kappa.pdf">An Analog of the Harmonic Numbers Over the Squarefree Integers</a>
%F a(n) = Numerator[(Sum_{k=1..n} mu^2(k)/phi(k)) - H_n] where mu(k) is the Mobius function, phi(k) is Euler's Totient function and H_n is the n-th Harmonic Number.
%e Numerators of F_n - H_n, e.g. - F_1 - H_1 = (1/1-1/1), F_2 = ((1/1-1/1) + (1/1-1/2)),...
%e F_11 = ((1/1-1/1) +(1/1-1/2) +(1/2-1/3) +(0-1/4) +(1/4-1/5) +(1/2-1/6) +(1/6-1/7) +(0-1/8) +(0-1/9) +(1/4-1/10) +(1/10-1/11)).
%t Table[Numerator[Sum[MoebiusMu[k]^2/EulerPhi[k], {k, 1, n}]-HarmonicNumber[n]], {n, 1, 60}]
%o (PARI) for(n=1,60, print1(numerator(sum(k=1,n, moebius(k)^2/eulerphi(k)) - sum(j=1,n,1/j)), ", ")) \\ _G. C. Greubel_, Aug 31 2018
%Y Cf. A138312, A138313, A138312, A138316, A138317, A138321, A083343, A001620.
%K frac,nonn
%O 1,3
%A Dick Boland (abstract(AT)imathination.org), Mar 14 2008, Mar 27 2008
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