generalized aliquot
koh
zbi74583 at boat.zero.ad.jp
Thu Jan 19 05:35:40 CET 2006
Hi, Seqfans
I defined {k,l}-Aliquot sequence as follows.
Let S_{k,l}(n)=1/l*Sigma(n)-k*n .
b(n)=S_{k,l}(b(n-1))
If b(n)=b(n+m) then it is called "{k,l}-Aliquot cycle" or "{k,l}-Sociable number of order m".
I will give some examples of {k,l}-Aliquot cycle.
These two sequences are S_{0,4} and S_{0,3}.
I did exhaustive search up to 10^6 for these sequences.
I feel a computer is too slow to calculate them.
Yasutoshi
----------
%I A000001
%S A000001 30240, 32760, 859320, 898560
%N A000001 Let S(n)=1/4*Sigma(n) .
Numbers such that S(S(n))=n, 1/4-Sociable number of order 1 or 2.
%C A000001 a(1) and a(2) are 4 multiple perfect numbers. a(4)=S(a(3)).
I calculated {2096640,2234232}. It is unknown if any pair exists between {a(3),a(4)} and this pair.
%H A000001 <a href="http://mathworld.wolfram.com/SociableNumbers.html">WathWorld</a>
%Y A000001 A000002
%K A000001 none
%O A000001 1,1
%A A000001 Yasutsohi Kohmoto zbi74583 at boat.zero.ad,jp
%I A000002
%S A000002 120, 672, 7680, 8184, 523776
%N A000002 Let S(n)=1/3*Sigma(n) .
Numbers such that S(S(n))=n, 1/3-Sociable number of oorder 1 or 2.
%C A000002 a(1) and a(2) and a(5) are 3 multiple perfect numbers. a(4)=S(a(3)).
%H A000002 <a href="http://mathworld.wolfram.com/SociableNumbers.html">WathWorld</a>
%Y A000002 A000001
%K A000002 none
%O A000002 1,1
%A A000002 Yasutoshi Kohmoto zbi74583 at boat.zero.ad,jp
More information about the SeqFan
mailing list