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

1, 2, 4, 8, 16, 32, 64, 80, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592

Offset: 1

Author

Michel Lagneau, May 12 2016

Keywords

• nonn

Comments

The number 80 is probably the unique non-power of 2 in the sequence.

Examples

			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.
		

Crossrefs

Cf. A000079, A006577.

Programs

Maple

with(numtheory):nn:=10000:
  for n from 1 to nn do:
    m:=n:it:=0:lst:={n}:
      for i from 1 to nn while(m<>1) do:
        if irem(m,2)=0
         then
         m:=m/2:
         else
         m:=3*m+1:
        fi:
       it:=it+1:lst:=lst union {m}:
      od:
       x:=divisors(n):n0:=nops(x):lst1:={op(x),x[n0]}:
       lst2:=lst intersect lst1:n1:=nops(lst2):
       if it+1=n1 and n0=n1
       then
       print(n):
       else fi:
     od: