20190714, 09:04  #1 
Nov 2016
23×97 Posts 
Quasialiquot Sequences?
In mathematics, a "quasiperfect number" is a natural number n for which n is the sum of its nontrivial divisors (i.e., its divisors excluding 1 and n), similarly, we define "quasialiquot sequence", a quasialiquot sequence is a sequence of positive integers in which each term is the sum of the nontrivial divisors (i.e., its divisors excluding 1 and n) of the previous term. e.g. the quasialiquot sequence of 36 is 36, 54, 65, 18, 20, 21, 10, 7, 0. Does quasialiquot sequence always end with either 0 or quasiamicable pair (betrothed pair, such as 48 and 75)?
Last fiddled with by sweety439 on 20190714 at 09:13 
20190714, 10:12  #2 
Oct 2011
2^{4}·3·7 Posts 
I know at least one more quasi 8cycles :
0 1270824975 1 1467511664 2 1530808335 3 1579407344 4 1638031815 5 1727239544 6 1512587175 7 1215571544 8 1270824975 9 1467511664 10 1530808335 11 1579407344 ... ... I had done many tests a few years ago with different iterative processes : n > s(n) + b s(n)=sigma(n)n If b=0 : aliquot sequences If b=1 : quasialiquot sequences For example, if b=38, it exists a 298cycle !!! You can see on this page, but sorry, in french (s(n) is called sigma'(n) on this page) : http://www.aliquotes.com/autres_proc...iteratifs.html I had even tried to extend the sigma function to something other than integers, such as polynomials, or Gauss integers. But the problem is that there is always something of the conventional order in these last cases, see here : http://www.aliquotes.com/etendre_sigma.html 
20200621, 21:45  #3 
Nov 2016
23·97 Posts 
Conjecture: there are no quasi ncycles if n is odd, specially, there are no quasiperfect numbers.

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