[seqfan] Re: nth divisor of a number

Maximilian Hasler maximilian.hasler at gmail.com
Fri Mar 30 05:20:13 CEST 2012

According to numerical data (which does not seem to
vary when I change the interval from [1..1e6] to [1..1e7]),

it seems that the 5th divisor is most likely to be 6
(in about 20% of the cases, followed by 8 and 16 in 6% of the cases)

and the 6th divisor is most likely to be 8 (in 9% of the cases)
(closely followed in likelihood by 10, in  ~7.5% of the cases).

Maximilian

Counts for 5th divisor, per 1000:
0, 0, 0, 0, 42, 211, 36, 60, 52, 48, 35, 0, 29, 27, 34, 60, 20, 0, 18,
0, 19, 15, 15, 0, 19, 11, 7, 0, 12, 0, 11,...
(i.e. 1,2,3,4 occur in 0% of the cases, 5 occurs in 4.2% of the cases, etc...)

Counts for 6th divisor, per 1000:
0, 0, 0, 0, 0, 49, 35, 91, 51, 77, 19, 51, 14, 55, 10, 12, 16, 44, 12,
31, 12, 28, 9, 0, 10, 22, 11, 20, 7, 0, 6, 28, 10,...

These percentages are of course approximate, calculated by neglecting
cases where the 5th resp. 6th divisor is > 100.

c=vector(100);for(n=1,1e7,5<#(d=divisors(n)) & d[6]<#c & c[d[6]]++)
c*1e3\sum(i=1,#c,c[i])

On Thu, Mar 29, 2012 at 10:52 PM, Marc LeBrun <mlb at well.com> wrote:
>>="Alonso Del Arte" <alonso.delarte at gmail.com>
>
> Interesting puzzle!
>
> My first guess would be the n-th divisor of A061799(n), but...
>
>
>
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