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

Author

Michel Lagneau, May 19 2013

Keywords

• nonn

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,...

Examples

			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.
		

Crossrefs

Cf. A225784, A225761.

Programs

Mathematica

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