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 A254196 a(n) is the numerator of Product_{i=1..n} (1/(1-1/prime(i))) - 1. 3
 1, 2, 11, 27, 61, 809, 13945, 268027, 565447, 2358365, 73551683, 2734683311, 112599773191, 4860900544813, 9968041656757, 40762420985117, 83151858555707, 5085105491885327, 341472595155548909, 24295409051193284539 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The denominators are A038110(n+1). 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. Appears to be a duplicate of A161527. - Michel Marcus, Aug 05 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..422 Eric Weisstein's World of Mathematics, Smooth Number FORMULA a(n) = A038111(n+1)/prime(n+1)-A038110(n+1). - Robert Israel, Jan 28 2015, corrected Jul 07 2019. EXAMPLE 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. MAPLE seq(numer(mul(1/(1-1/ithprime(i)), i=1..n)-1), n=1..20); # Robert Israel, Jan 28 2015 MATHEMATICA 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] Numerator@ Table[b[n], {n, 1, 20}] (* Fred Daniel Kline, Jun 27 2017 *) PROG (PARI) a(n) = numerator(prod(i=1, n, (1/(1-1/prime(i)))) - 1); \\ Michel Marcus, Jun 29 2017 CROSSREFS Cf. A038110, A000079, A003586, A051037, A002473, A051038, A161527. Sequence in context: A141464 A218471 A139211 * A161527 A143651 A054552 Adjacent sequences:  A254193 A254194 A254195 * A254197 A254198 A254199 KEYWORD nonn AUTHOR Geoffrey Critzer, Jan 26 2015 STATUS approved

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Last modified May 6 16:20 EDT 2021. Contains 343586 sequences. (Running on oeis4.)