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A236435
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Numerator of product_{k=1..n-1} (1 + 1/prime(k)).
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7
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1, 3, 2, 12, 96, 1152, 2304, 41472, 165888, 3981312, 119439360, 3822059520, 7644119040, 321052999680, 1284211998720, 61642175938560, 3328677500682240, 199720650040934400, 399441300081868800, 1597765200327475200, 115039094423578214400, 230078188847156428800, 18406255107772514304000
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OFFSET
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1,2
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979; Theorem 429.
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LINKS
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FORMULA
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a(n) / A236436(n) = product_{k=1..n-1} (1 + 1/prime(k)) ~ (6/Pi^2)*exp(gamma)*log(n) as n -> infinity, by Mertens' theorem.
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EXAMPLE
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(1 + 1/2)*(1 + 1/3)*(1 + 1/5)*(1 + 1/7) = 96/35 has numerator a(5) = 96.
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MATHEMATICA
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Numerator@Table[ Product[ 1 + 1/Prime[ k], {k, 1, n-1}], {n, 1, 23}]
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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