[seqfan] Re: Record values of sigma(n+1)/sigma(n)
Charles Greathouse
charles.greathouse at case.edu
Mon Oct 4 15:03:13 CEST 2010
Looking at A004394, I can see that 130429015516799 is a member of the
sequence with sigma(n+1)/sigma(n) > 6. Similarly,
9854961523502269526351999 for 7,
12334037514864599053024743931236692051903999 for 8,
6553386545032231213471815304698770482991672570850940874249785314181055999
for 9, and 1654561128226196128845909933761934649700488343804541949950770032612220138050084647974939320138356724706447331227979902261929221509759999
for 10.
I don't much like the notation d(n), which can be confused for A000005.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Mon, Oct 4, 2010 at 2:59 AM, zak seidov <zakseidov at yahoo.com> wrote:
>
> %N A1 Integers n with record values of
> d(n) = sigma(n+1)/sigma(n).
>
> n, d(n)
> 1, 3
> 179, 91/30,
> 239, 31/10,
> 359, 13/4,
> 719, 403/120,
> 839, 24/7,
> 1259, 52/15,
> 3359, 18/5,
> 5039, 403/105,
> 10079, 39/10,
> 25199, 12493/3192,
> 27719, 520/131,
> 50399, 8463/2125,
> 55439, 1612/385,
> 110879, 234/55,
> 166319, 992/231,
> 360359, 65520/15109,
> 665279, 1016/231,
> 831599, 15376/3465,
> 1081079, 640/143,
> 1441439, 252/55,
> 2162159, 20832/4511,
> 3603599, 699608/150335,
> 4324319, 1008/215,
> 12972959, 308/65,
> 21621599, 62496/12877,
> 43243199, 440944/90423,
> 61261199, 23064/4675,
> 73513439, 37632/7571,
> 122522399, 12796056/2553035,
> 205405199, 615040/122293,
> 245044799, 12897612/2559509,
> 410810399, 13888/2717,
> 698377679, 238080/46189,
> 735134399, 62992/12155
>
> The last value of d(n)=
> 62992/12155=
> 5.182394076511723570547099959
>
> 1. More terms?
> 2. Can we reach, say, d>6?
> 3. Is any limit for d(n) with n--> inf?
>
> Thanks,
> Zak
>
>
>
>
>
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