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A074738
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Decimal expansion of d = 1-(1+log(log(2)))/log(2) = 0.08607133....
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2
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0, 8, 6, 0, 7, 1, 3, 3, 2, 0, 5, 5, 9, 3, 4, 2, 0, 6, 8, 8, 7, 5, 7, 3, 0, 9, 8, 7, 7, 6, 9, 2, 2, 6, 7, 7, 7, 6, 0, 5, 9, 1, 1, 0, 9, 5, 3, 0, 3, 3, 3, 1, 7, 3, 4, 9, 2, 0, 2, 0, 2, 3, 6, 6, 6, 5, 4, 2, 2, 6, 3, 5, 8, 1, 4, 6, 2, 2, 8, 7, 9, 7, 9, 9, 3, 8, 0, 5, 3, 4, 6, 0, 2, 5, 2, 8, 7, 6, 8, 0, 7, 1, 6, 3
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OFFSET
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0,2
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COMMENTS
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An Erdős constant: let s(x) denotes the number of numbers < x expressible as a product of 2 numbers less than or equal to sqrt(x). Erdős showed that S(x) is x/(log x)^(d+o(1)) where d is this constant.
Ford finds that, if H(x,y,z) is the number of integers n <= x which have a divisor in the interval (y,z] and for 3 <= y <= sqrt(x), H(x,y,2y) = x/(((log y)^delta)(log log y)^(3/2)) where delta is the Erdős constant whose decimal digits are A074738. - Jonathan Vos Post, Jul 19 2007
Luca & Pomerance call this the Erdős-Tenenbaum-Ford constant and show its relationship to the reduced totient function A002174. - Charles R Greathouse IV, Dec 28 2013
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LINKS
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Dimitris Koukoulopoulos, Divisors of shifted primes, arXiv:0905.0163 [math.NT], 2009-2010; International Mathematics Research Notices, 2010:24, pp. 4585-4627.
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MAPLE
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MATHEMATICA
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Join[{0}, RealDigits[1 - (1 + Log[Log[2]])/Log[2], 10, 100][[1]]] (* G. C. Greubel, Apr 16 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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