login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236436 Denominator of product_{k=1..n-1} (1 + 1/prime(k)). 8

%I #15 Feb 14 2014 07:50:27

%S 1,2,1,5,35,385,715,12155,46189,1062347,30808063,955049953,1859834119,

%T 76253198879,298080686527,14009792266769,742518990138757,

%U 43808620418186663,86204059532560853,339745411098916303,24121924188023057513,47591904479072518877,3759760453846728991283

%N Denominator of product_{k=1..n-1} (1 + 1/prime(k)).

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979; Theorem 429.

%H Vincenzo Librandi, <a href="/A236436/b236436.txt">Table of n, a(n) for n = 1..200</a>

%H J. Sondow and E. Weisstein, <a href="http://mathworld.wolfram.com/MertensTheorem.html">MathWorld: Mertens Theorem</a>

%F A236435(n+1) / a(n+1) = A072045(n)/A072044(n) / A038110(n+1)/A060753(n+1) because 1+x = (1-x^2) / (1-x).

%F A236436(n) / a(n) = product_{k=1..n-1} (1 + 1/prime(k)) ~ (6/Pi^2)*exp(gamma)*log(n) as n -> infinity, by Mertens' theorem.

%e (1 + 1/2)*(1 + 1/3)*(1 + 1/5)*(1 + 1/7) = 96/35 has denominator a(5) = 35.

%t Denominator@Table[Product[1 + 1/Prime[k], {k, 1, n - 1}], {n, 1, 23}]

%Y Cf. A038110, A060753, A072044, A072045, A236435.

%K nonn,frac

%O 1,2

%A _Jonathan Sondow_, Feb 01 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)