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A161527
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Numerators of cumulative sums of rational sequence A038110(k)/A038111(k).
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5
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1, 2, 11, 27, 61, 809, 13945, 268027, 565447, 2358365, 73551683, 2734683311, 112599773191, 4860900544813, 9968041656757, 40762420985117, 83151858555707, 5085105491885327, 341472595155548909, 24295409051193284539, 1777124696397561611347
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OFFSET
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1,2
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COMMENTS
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By rewriting the sequence of sums as 1 - Product_{n>=1} (1 - 1/prime(n)), one can show that the product goes to zero and the sequence of sums converges to 1. This is interesting because the terms approach 1/(2*prime(n)) for large n, and a sum of such terms might be expected to diverge, since Sum_{n>=1} 1/(2*prime(n)) diverges.
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LINKS
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FORMULA
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MATHEMATICA
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Table [1- Product[1 - (1/Prime[k])), {i, 1, j}, {j, 1, 20}]; (* This is a table of the individual sums: Sum[Product[ 1 - (1/Prime[k]), {k, n-1}]/Prime[n], {n, 1, 3}], which is the sum of terms of the Mathematica table given in A038111 (three terms, in this example). *)
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PROG
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(PARI) r(n) = prod(k=1, n-1, (1 - 1/prime(k)))/prime(n);
a(n) = numerator(sum(k=1, n, r(k))); \\ Michel Marcus, Jun 08 2019
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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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