OFFSET
1,2
COMMENTS
Partial sums of the reciprocals of (perfect powers -- squares, cubes, etc. -- plus 1).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..420
FORMULA
a(n) = numerator(Sum_{k=1..n} 1/A216765(k)).
Limit_{n->oo} a(n)/A216767(n) = Pi^2/3 - 5/2. - Amiram Eldar, May 05 2022
EXAMPLE
The partial sums are of the sequence of fractions: 1/5 + 1/9 + 1/10 + 1/17 + 1/26 + 1/28 + 1/33 + 1/37 + 1/50, ... and thus the partial sums are 1/5, 14/45, 37/90, 719/1530, 5056/9995, 151513/278460, 1759463/3063060, 68163191/113333220, 352149277/566666100, 360867217/566666100, 15078888947/23233310100, ...
MATHEMATICA
Numerator[FoldList[Plus, 1/(1 + Select[Range[250], GCD @@ FactorInteger[#][[;; , 2]] > 1 &])]] (* Amiram Eldar, May 05 2022 *)
CROSSREFS
KEYWORD
easy,nonn,frac
AUTHOR
Jonathan Vos Post, Sep 15 2012
STATUS
approved