A114998 a(n) = numerator of Sum_{i=1..n} +-1/n, where the sign is -1 iff n is prime.

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

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..30.

Example

The partial sums are 1, 1/2, 1/6, 5/12, 13/60, 23/60, 101/420, 307/840, 1201/2520, 1453/2520, ...

Maple

f:=proc(n) if isprime(n) then -1/n else 1/n fi; end; g:=proc(n) add(f(i), i=1..n); end;

Mathematica

Table[Numerator[HarmonicNumber[n] - 2*Sum[1/Prime[i], {i, 1, PrimePi[n]}]], {n, 1, 30}] (* Stefan Steinerberger, Feb 23 2006 *)
Accumulate[Table[If[PrimeQ[n], -1/n, 1/n], {n, 30}]]//Numerator (* Harvey P. Dale, Aug 13 2021 *)

Crossrefs

Sequence in context: A083800 A075829 A119248 * A340564 A140090 A271937

Adjacent sequences: A114995 A114996 A114997 * A114999 A115000 A115001

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 23 2006

Status

approved