

A225878


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


0



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
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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 nonpowers 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 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: A036135 A036131 A115424 * A323097 A272985 A318588
Adjacent sequences: A225875 A225876 A225877 * A225879 A225880 A225881


KEYWORD

nonn


AUTHOR

Michel Lagneau, May 19 2013


STATUS

approved



