Search: id:A024451
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%I A024451
%S A024451 1,5,31,247,2927,40361,716167,14117683,334406399,9920878441,314016924901,
%T A024451 11819186711467,492007393304957,21460568175640361,1021729465586766997,
%U A024451 54766551458687142251,3263815694539731437539,201015517717077830328949
%N A024451 Numerator of Sum_{i = 1..n} 1/prime(i).
%C A024451 Arithmetic derivative of p#: a(n) = A003415(A002110(n)). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Feb 25 2002
%D A024451 S. R. Finch, Mathematical Constants, Cambridge, 2003, Sect. 2.2.
%D A024451 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Sect. VII.28.
%H A024451 T. D. Noe, <a href="b024451.txt">Table of n, a(n) for n=1..100</a>
%F A024451 lim_{n -> infinity} (Sum_{p <= n} 1/p - log log n) = 0.2614972... = A077761.
%F A024451 a(n) = prod_{i=1, n} prime(i))*sum(i=1, n, 1/prime(i)) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Jan 30 2002
%F A024451 (n+1)-st elementary symmetric function of the first n primes.
%F A024451 a(n) = a(n-1)*A000040(n) + A002110(n-1) - Henry Bottomley (se16(AT)btinternet.com), 
               Sep 27 2006
%e A024451 1/2, 5/6, 31/30, 247/210, 2927/2310, 40361/30030, 716167/510510, 14117683/
               9699690, ...
%Y A024451 Denominators are A002110. See also A106830/A034386.
%Y A024451 Sequence in context: A062147 A069321 A082579 this_sequence A046852 A056541 
               A126121
%Y A024451 Adjacent sequences: A024448 A024449 A024450 this_sequence A024452 A024453 
               A024454
%K A024451 nonn,frac,easy,nice
%O A024451 1,2
%A A024451 N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)

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