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Search: id:A114998
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| A114998 |
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a(n) = numerator of Sum_{i=1..n} +-1/n, where the sign is -1 iff n is prime. |
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+0
1
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| 1, 1, 1, 5, 13, 23, 101, 307, 1201, 1453, 13463, 15773, 177329, 203069, 227093, 499231, 7766207, 938543, 16470957, 17764249, 56987867, 60515027, 1314248101, 462870797, 2433336849, 2547743449, 71763644723, 74631981623, 2084014033867, 2161650352627
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The denominators are given by A003418.
The sum diverges. In fact, the n-th partial sum is C_1 log n - C2 log log n, regardless of ordering, which can only affect c1 and c2. - R. K. Guy.
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EXAMPLE
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The partial sums are 1, 1/2, 1/6, 5/12, 13/60, 23/60, 101/420, 307/840, 1201/2520, 1453/2520, ...
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MAPLE
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f:=proc(n) if isprime(n) then -1/n else 1/n fi; end; g:=proc(n) add(f(i), i=1..n); end;
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MATHEMATICA
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Table[Numerator[HarmonicNumber[n] - 2*Sum[1/Prime[i], {i, 1, PrimePi[n]}]], {n, 1, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 23 2006
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CROSSREFS
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Sequence in context: A049833 A075829 A119248 this_sequence A140090 A121511 A004627
Adjacent sequences: A114995 A114996 A114997 this_sequence A114999 A115000 A115001
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KEYWORD
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nonn,frac
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AUTHOR
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njas, Feb 23 2006
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