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A226945
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Integer nearest f(10^n), where f(x) = Sum of ( mu(k) * H(k)/k^(3/2) * Integral Log(x^(1/k)) ) for k = 1 to infinity, where H(k) is the harmonic number sum_{i=1..k} 1/i.
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2
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4, 25, 168, 1226, 9585, 78521, 664652, 5761512, 50847348, 455050385, 4118051652, 37607908133, 346065524108, 3204941711340, 29844570436484, 279238341185832, 2623557156537070, 24739954282695698, 234057667295619287, 2220819602542218793
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OFFSET
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1,1
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COMMENTS
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The sequence gives exactly the values of pi(10^n) for n = 1 to 3.
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LINKS
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MATHEMATICA
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f[n_Integer] := Sum[N[MoebiusMu[k]*HarmonicNumber[k]/k^(3/2)*LogIntegral[n^(1/k)], 50], {k, 5!}]; Table[Round[f[10^n]], {n, 20}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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