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A024451
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Numerator of Sum_{i = 1..n} 1/prime(i).
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12
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1, 5, 31, 247, 2927, 40361, 716167, 14117683, 334406399, 9920878441, 314016924901, 11819186711467, 492007393304957, 21460568175640361, 1021729465586766997, 54766551458687142251, 3263815694539731437539, 201015517717077830328949
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Arithmetic derivative of p#: a(n) = A003415(A002110(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 25 2002)
(n-1)-st elementary symmetric functions of first n primes; see Mathematica section. [From Clark Kimberling, Dec 29 2011]
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REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge, 2003, Sect. 2.2.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Sect. VII.28.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
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FORMULA
| lim_{n -> infinity} (Sum_{p <= n} 1/p - log log n) = 0.2614972... = A077761.
a(n) = prod_{i=1, n} prime(i))*sum(i=1, n, 1/prime(i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 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 (se16(AT)btinternet.com), Sep 27 2006
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EXAMPLE
| 1/2, 5/6, 31/30, 247/210, 2927/2310, 40361/30030, 716167/510510, 14117683/9699690, ...
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MATHEMATICA
| a[n_] := Numerator @ Sum[1/Prime[i], {i, n}]; Array[a, 18] (* From 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 *)
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PROG
| (MAGMA) [ Numerator(&+[ NthPrime(k)^-1: k in [1..n]]): n in [1..18] ]; // Bruno Berselli, Apr 11 2011
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CROSSREFS
| Denominators are A002110. See also A106830/A034386.
Sequence in context: A177797 A186859 A082579 * A046852 A056541 A126121
Adjacent sequences: A024448 A024449 A024450 * A024452 A024453 A024454
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KEYWORD
| nonn,frac,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)
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