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 A060753 Denominator of 1*2*4*6*...*(prime(n-1)-1) / (2*3*5*7*...*prime(n-1)). 18
 1, 2, 3, 15, 35, 77, 1001, 17017, 323323, 676039, 2800733, 86822723, 3212440751, 131710070791, 5663533044013, 11573306655157, 47183480978717, 95993978542907, 5855632691117327, 392327390304860909 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, numerator of Product_{k=1..n-1} prime(k)/(prime(k)-1) (cf. A038110). - N. J. A. Sloane, Apr 17 2015 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 429 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..423 F. Ellermann, Illustration for A002110, A005867, A038110, A060753 J. Sondow and Eric Weisstein, Euler Product, MathWorld. FORMULA a(n) = A002110(n) / gcd( A005867(n), A002110(n) ). A038110(n) / a(n) ~ exp( -gamma ) / log( prime(n) ), Mertens's theorem for x = prime(n) = A000040(n). A038110(n) / a(n) = A005867(n) / A002110(n). - corrected by Simon Tatham, Jul 26 2016 a(n) = A038111(n) / prime(n). - Vladimir Shevelev, Jan 10 2014 a(n) = A038110(n) + A161527(n-1). - Jamie Morken, Jun 19 2019 EXAMPLE A038110(50)/ a(50) = 0.1020..., exp(-gamma)/log(229) = 0.1033... 1*2*4/(2*3*5) = 8/15 has denominator a(4) = 15. - Jonathan Sondow, Jan 31 2014 MATHEMATICA Table[Denominator@ Product[EulerPhi@ Prime[i]/Prime@ i, {i, n}], {n, 0, 19}] (* Michael De Vlieger, Jan 10 2015 *) {1}~Join~Denominator@ FoldList[Times, Table[EulerPhi@ Prime[n]/Prime@ n, {n, 19}]] (* Michael De Vlieger, Jul 26 2016 *) b[0] := 0; b[n_] := b[n - 1] + (1 - b[n - 1]) / Prime[n] Denominator@ Table[b[n], {n, 0, 20}] (* Fred Daniel Kline, Jun 27 2017 *) PROG (MAGMA) [1] cat [Denominator((&*[NthPrime(k-1)-1:k in [2..n]])/(&*[NthPrime(k-1):k in [2..n]])):n in [2..20]]; // Marius A. Burtea, Sep 19 2019 CROSSREFS Cf. A002110, A005867, A038110, A038111. Cf. A236435, A236436. Sequence in context: A064219 A244377 A244330 * A241198 A296296 A143880 Adjacent sequences:  A060750 A060751 A060752 * A060754 A060755 A060756 KEYWORD nonn,frac AUTHOR Frank Ellermann, Apr 23 2001 EXTENSIONS Definition corrected by Jonathan Sondow, Jan 31 2014 STATUS approved

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Last modified February 21 20:29 EST 2020. Contains 332111 sequences. (Running on oeis4.)