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Search: id:A024451
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| A024451 |
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Numerator of Sum_{i = 1..n} 1/prime(i). |
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+0
11
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| 1, 5, 31, 247, 2927, 40361, 716167, 14117683, 334406399, 9920878441, 314016924901, 11819186711467, 492007393304957, 21460568175640361, 1021729465586766997, 54766551458687142251, 3263815694539731437539, 201015517717077830328949
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Arithmetic derivative of p#: a(n) = A003415(A002110(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 25 2002
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n=1..100
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FORMULA
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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
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1/2, 5/6, 31/30, 247/210, 2927/2310, 40361/30030, 716167/510510, 14117683/9699690, ...
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CROSSREFS
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Denominators are A002110. See also A106830/A034386.
Sequence in context: A062147 A069321 A082579 this_sequence A046852 A056541 A126121
Adjacent sequences: A024448 A024449 A024450 this_sequence A024452 A024453 A024454
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KEYWORD
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nonn,frac,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)
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