gaps in sigma()

[Max]

Jud McCranie wrote:
> At 06:13 PM 8/8/2005, Max wrote:
>> Let a=a(n) be the minimum positive integer such that [a,a+n-1] does 
>> not contain any values of sigma(k) (i.e., sum of all positive divisors 
>> of k).
>> According to http://www.mathlinks.ro/Forum/viewtopic.php?t=26906 the 
>> initial terms of a(n) are
>> 2, 9, 49, 423, 1333
>>
>> Would anybody like to extend and/or submit this sequence to OEIS?
> 
> I get
> 2,9,9,49,49,423,423,423,423,1333,1333,4425,4425,4425,4425,8763,8763,
> 14089,14089,22825,22825,22825,22825,40291,40291,40291,40291,40291,
> 40291,178705,178705,661285,661285,661285,661285,4543141,4543141
> 
> and the next 10 terms are also 4543141

It makes sense to add two more sequences:

sequences a(n) after eliminating duplicate terms (i.e., increasing gaps starting positions)
b(n) = 2, 9, 49, 423, 1333, 4425, ...

associated gap length
c(n) = 1, 3, 5, 9, 11, ...

They are related as
c(n) = maximum m such that a(m)=b(n)

Max