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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. 1
 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 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: A115424 A225878 A323097 * 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 October 15 13:38 EDT 2019. Contains 328030 sequences. (Running on oeis4.)