A216766 Numerators of partial sums of 1/A216765(n).

1, 14, 37, 719, 5056, 151513, 1759463, 68163191, 352149277, 360867217, 15078888947, 1546201093747, 95491548878617, 10736398220663, 1400899861968427, 41036431877859203, 41386424246755373, 8212624279323157381, 256265816149636840711, 29139716513641120366493

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

Cf. A001597, A045542, A175064, A214390, A214391, A216765, A216767 (denominators).

Sequence in context: A121319 A361994 A034181 * A057439 A256560 A058826

Adjacent sequences: A216763 A216764 A216765 * A216767 A216768 A216769

Keyword

easy,nonn,frac

Author

Jonathan Vos Post, Sep 15 2012

Status

approved