A225878 Numbers n such that the products n*(sum of the reciprocals of the Collatz (3x+1) sequence beginning at n) are integers.

1, 2, 4, 8, 16, 32, 64, 80, 128, 160, 208, 256, 320, 416, 512, 640, 832, 1024, 1280, 1344, 1664, 2048, 2560, 2688, 3328, 4096, 5120, 5376, 6656, 8192, 10240, 10752, 13312, 16384, 20480, 21504, 21760, 26624, 27264, 32768, 40960, 43008, 43520, 53248, 54528

Offset

1,2

Comments

Numbers n such that A225784(n) divides n.

The powers of 2 are in the sequence, but there exists a subsequence of non-powers of 2: 80, 160, 208, 320, 416, 640, 832, 1280, 1344,... where the members are of the forms 5*2^p with p>=4, 13*2^p with p>=4, 21*2^p with p>=6, 213*2^p with p>=7, 341*2^p with p>=10,...

Links

Table of n, a(n) for n=1..45.

Example

208 is in the sequence because 208 *(1/208 + 1/104 + 1/52 + 1/26 + 1/13 + 1/40 + 1/20 + 1/10 + 1/5 + 1/16 + 1/8 + 1/4 +1/2 + 1/1) = 512 is an integer.
2688 is in the sequence because A225784(2688) = 896 divides 2688.

Mathematica

collatz[n_]:=NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; Select[Range[50000], IntegerQ[Total[#/collatz[#]]]&]

Crossrefs

Cf. A225784, A225761.

Sequence in context: A115424 A372944 A381069 * A323097 A272985 A318588

Adjacent sequences: A225875 A225876 A225877 * A225879 A225880 A225881

Keyword

nonn

Author

Michel Lagneau, May 19 2013

Status

approved