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A272985 Numbers n such that the elements of the Collatz trajectory of n are exactly the same as the divisors of n.

%I A272985 #14 May 22 2016 09:33:39
%S A272985 1,2,4,8,16,32,64,80,128,256,512,1024,2048,4096,8192,16384,32768,
%T A272985 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A272985 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592
%N A272985 Numbers n such that the elements of the Collatz trajectory of n are exactly the same as the divisors of n.
%C A272985 The number 80 is probably the unique non-power of 2 in the sequence.
%e A272985 80 is in the sequence because 80 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 with 9 iterations and the divisors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
%p A272985 with(numtheory):nn:=10000:
%p A272985   for n from 1 to nn do:
%p A272985     m:=n:it:=0:lst:={n}:
%p A272985       for i from 1 to nn while(m<>1) do:
%p A272985         if irem(m,2)=0
%p A272985          then
%p A272985          m:=m/2:
%p A272985          else
%p A272985          m:=3*m+1:
%p A272985         fi:
%p A272985        it:=it+1:lst:=lst union {m}:
%p A272985       od:
%p A272985        x:=divisors(n):n0:=nops(x):lst1:={op(x),x[n0]}:
%p A272985        lst2:=lst intersect lst1:n1:=nops(lst2):
%p A272985        if it+1=n1 and n0=n1
%p A272985        then
%p A272985        print(n):
%p A272985        else fi:
%p A272985      od:
%Y A272985 Cf. A000079, A006577.
%K A272985 nonn
%O A272985 1,2
%A A272985 _Michel Lagneau_, May 12 2016