This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A024451 a(n) is the numerator of Sum_{i = 1..n} 1/prime(i). 34
 0, 1, 5, 31, 247, 2927, 40361, 716167, 14117683, 334406399, 9920878441, 314016924901, 11819186711467, 492007393304957, 21460568175640361, 1021729465586766997, 54766551458687142251, 3263815694539731437539, 201015517717077830328949, 13585328068403621603022853 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Arithmetic derivative of p#: a(n) = A003415(A002110(n)). - Reinhard Zumkeller, Feb 25 2002 (n-1)-st elementary symmetric functions of first n primes; see Mathematica section. - Clark Kimberling, Dec 29 2011 Denominators of the harmonic mean of the first n primes. - Colin Barker, Nov 14 2014 Let Pn(n) = A002110 denote the primorial function. The average number of distinct prime factors <= prime(n) in the natural numbers up to Pn(n) is equal to Sum_{i = 1..n} 1/prime(i). - Jamie Morken, Sep 17 2018 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Sect. 2.2. D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Sect. VII.28. LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..350 (terms n = 1..100 from T. D. Noe) FORMULA lim_{n -> infinity} (Sum_{p <= n} 1/p - log log n) = 0.2614972... = A077761. a(n) = (Product_{i=1..n} prime(i))*(Sum_{i=1..n} 1/prime(i)). - Benoit Cloitre, Jan 30 2002 (n+1)-st elementary symmetric function of the first n primes. a(n) = a(n-1)*A000040(n) + A002110(n-1). - Henry Bottomley, Sep 27 2006 EXAMPLE 0/1, 1/2, 5/6, 31/30, 247/210, 2927/2310, 40361/30030, 716167/510510, 14117683/9699690, ... MAPLE h:= n-> add(1/(ithprime(i)), i=1..n); t1:=[seq(h(n), n=0..50)]; t1a:=map(numer, t1); # A024451 t1b:=map(denom, t1); # A002110 - N. J. A. Sloane, Apr 25 2014 MATHEMATICA a[n_] := Numerator @ Sum[1/Prime[i], {i, n}]; Array[a, 18]  (* Jean-François Alcover, Apr 11 2011 *) f[k_] := Prime[k]; t[n_] := Table[f[k], {k, 1, n}] a[n_] := SymmetricPolynomial[n - 1, t[n]] Table[a[n], {n, 1, 16}] (* A024451 *) (* Clark Kimberling, Dec 29 2011 *) Numerator[Accumulate[1/Prime[Range[20]]]] (* Harvey P. Dale, Apr 11 2012 *) PROG (MAGMA) [ Numerator(&+[ NthPrime(k)^-1: k in [1..n]]): n in [1..18] ];  // Bruno Berselli, Apr 11 2011 (PARI) a(n) = numerator(sum(i=1, n, 1/prime(i))); \\ Michel Marcus, Sep 18 2018 CROSSREFS Denominators are A002110. See also A106830/A034386, A241189/A241190, A241191/A241192, A061015/A061742, A115963/A115964, A250133/A296358. Sequence in context: A294214 A261498 A276312 * A046852 A056541 A291885 Adjacent sequences:  A024448 A024449 A024450 * A024452 A024453 A024454 KEYWORD nonn,frac,easy,nice AUTHOR EXTENSIONS a(0)=0 prepended by Alois P. Heinz, Jun 26 2015 STATUS approved

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

Last modified January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)