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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A036131 A115424 A225878 * A318588 A008881 A208743

Adjacent sequences:  A272982 A272983 A272984 * A272986 A272987 A272988

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 12 2016

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)