[seqfan] Re: Record values of sigma(n+1)/sigma(n)

[Robert Gerbicz]

2010/10/4 zak seidov <zakseidov at yahoo.com>

>
> %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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There is no limit, let n=p prime for that p+1 is divisible by the first k
primes (from Dirichlet theorem there are infinite many such primes).