This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225878 #8 Jan 08 2025 13:01:29 %S A225878 1,2,4,8,16,32,64,80,128,160,208,256,320,416,512,640,832,1024,1280, %T A225878 1344,1664,2048,2560,2688,3328,4096,5120,5376,6656,8192,10240,10752, %U A225878 13312,16384,20480,21504,21760,26624,27264,32768,40960,43008,43520,53248,54528 %N A225878 Numbers n such that the products n*(sum of the reciprocals of the Collatz (3x+1) sequence beginning at n) are integers. %C A225878 Numbers n such that A225784(n) divides n. %C A225878 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,... %e A225878 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. %e A225878 2688 is in the sequence because A225784(2688) = 896 divides 2688. %t A225878 collatz[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&];Select[Range[50000],IntegerQ[Total[#/collatz[#]]]&] %Y A225878 Cf. A225784, A225761. %K A225878 nonn %O A225878 1,2 %A A225878 _Michel Lagneau_, May 19 2013