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A254196
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a(n) is the numerator of Product_{i=1..n} (1/(1-1/prime(i))) - 1.
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3
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1, 2, 11, 27, 61, 809, 13945, 268027, 565447, 2358365, 73551683, 2734683311, 112599773191, 4860900544813, 9968041656757, 40762420985117, 83151858555707, 5085105491885327, 341472595155548909, 24295409051193284539
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OFFSET
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1,2
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COMMENTS
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a(n)/A038110(n+1) = Sum_{k >=2} 1/k where k is a positive integer whose prime factors are among the first n primes. In particular, for n=1,2,3,4,5, a(n)/A038110(n+1) is the sum of the reciprocals of the terms (excepting the first, 1) in A000079, A003586, A051037, A002473, A051038.
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LINKS
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FORMULA
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EXAMPLE
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a(1)=1 because 1/2 + 1/4 + 1/8 + 1/16 + ... = 1/1.
a(2)=2 because 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/9 + 1/12 + ... = 2/1.
a(3)=11 because 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/8 + 1/9 + 1/10 + 1/12 + 1/15 + ... = 11/4.
a(4)=27 because Sum_{n>=2} 1/A002473(n) = 27/8.
a(5)=61 because Sum_{n>=2} 1/A051038(n) = 61/16.
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MAPLE
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seq(numer(mul(1/(1-1/ithprime(i)), i=1..n)-1), n=1..20); # Robert Israel, Jan 28 2015
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MATHEMATICA
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Numerator[Table[Product[1/(1 - 1/p), {p, Prime[Range[n]]}] - 1, {n, 1, 20}]]
b[0] := 0; b[n_] := b[n - 1] + (1 - b[n - 1]) / Prime[n]
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PROG
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(PARI) a(n) = numerator(prod(i=1, n, (1/(1-1/prime(i)))) - 1); \\ Michel Marcus, Jun 29 2017
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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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