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

1,2

Comments

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

Links

Table of n, a(n) for n=1..35.

Example

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.

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:

Crossrefs

Cf. A000079, A006577.

Sequence in context: A372944 A225878 A323097 * A318588 A008881 A208743

Adjacent sequences: A272982 A272983 A272984 * A272986 A272987 A272988

Keyword

nonn

Author

Michel Lagneau, May 12 2016

Status

approved