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A222761
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Conjectured lower bounds for the Riemann hypothesis function floor(H(k) + exp(H(k))*log(H(k))) - sigma(k).
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2
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0, 1, 2, 6, 23, 33, 34, 78, 105, 207, 492, 1536, 1667, 3036, 5155, 5206, 7682, 8748, 9051, 15895, 21295, 22160, 36300, 58331, 58657, 71186, 81276, 91902, 126789, 142721, 143828, 240466, 291217, 306310, 471093, 743434, 872803, 963860, 1652806, 1742555
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OFFSET
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1,3
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COMMENTS
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Here H(k) is the k-th harmonic number, sum_{i=1..k) 1/i, and sigma(k) is the sum of the divisors of k. This sequence gives the conjectured values of A057641 that form a lower bound. For instance,
all numbers x <= 0 appear for n <= 12 = A176679(3);
all numbers x <= 1 appear for n <= 24 = A176679(4);
all numbers x <= 2 appear for n <= 60 = A176679(5);
all numbers x <= 6 appear for n <= 120 = A176679(6);
all numbers x <= 23 appear for n <= 180 = A176679(7).
The pattern continues.
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LINKS
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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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