# Value a(6) in doubt for a =

Maximilian Hasler maximilian.hasler at gmail.com
Tue Jan 15 13:31:05 CET 2008

```I rather get too much for the sum of reciprocals of the given elements
(6.02 ; exact fraction given below) :

{a6 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52,
53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
72, 74, 75, 76, 77, 78, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93,
94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 114, 115,
116, 117, 119, 120, 121, 122, 123, 124, 126, 128, 129, 130, 132, 133,
134, 136, 138, 140, 141, 143, 145, 147, 148, 150, 152, 153, 155, 156,
159, 161, 162, 164, 168, 170, 171, 174, 177, 180, 182, 183, 184, 185,
186, 187, 188, 190, 192, 196, 201, 203, 204, 205, 207, 209, 210, 212,
215, 217, 221, 222, 228, 230, 232, 238, 242, 245, 246, 247, 248, 250,
252, 253, 255, 258, 259, 261, 266, 268, 272, 276, 280, 282, 285, 287,
290, 294, 295, 299, 301, 304, 305, 306, 310, 315, 319, 322, 323, 324,
328, 329, 341, 344, 345, 348, 354, 360, 363, 368, 370, 372, 375, 376,
377, 380, 384, 387, 402, 406, 407, 413, 414, 424, 430, 434, 435, 444,
451, 460, 465, 469]}

(08:48) gp > #a6
%68 = 231

(08:48) gp > sum(i=1,#a6,1/i)
%69 = 1656004646976728279947182788218449721292751379533929572022380425777900266075898403119911523294643463
/ 275001770253164763004063109464518007415669656915565314578673311665481739895263338101920366994736000

(08:48) gp > %*1.
%70 = 6.0217963159008818116821418831900358255

Regards,
Maximilian

On Jan 14, 2008 12:46 PM, Rainer Rosenthal <r.rosenthal at web.de> wrote:
> The values of
> http://www.research.att.com/~njas/sequences/A101877
> are defined as  a(n) = max(S_n) where the sum of
> reciprocals of S_n is n. It is claimed that no S_n
> with smaller maximum could be found.
>
> I checked
>
>         ReciprocalSum(S_n) = n
>
> for n=1..6 and it was correct for n=1..5 but incorrect
> for n=6:
>
>     ReciprocalSum(S_6) is less than 6 (about 5.76).
>
> I wasn't able to guess what's wrong with S_6 but following
> a remark about the inclusion of S_n in S_{n+1} I checked
> whether S_5 was a subset of the S_6, given there. An no,
> it is not. S_6 lacks {80, 112, 144, 154, 165, 175, 176},
> but adding these is not enough.
>
> How to repair the description of A101877 and confirm
> a(6) = 469?
>
> Rainer Rosenthal
> r.rosenthal at web.de
>
>
>
>

--
Maximilian F. Hasler (Maximilian.Hasler(AT)gmail.com)

```