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n+floor(nr/t)+floor(ns/t), where r=2^(1/2), s=2^(1/3), t=2^(1/5).
3

%I #4 Mar 30 2012 18:57:17

%S 3,6,9,12,16,19,22,25,29,32,36,39,43,46,49,52,55,59,62,65,69,73,76,79,

%T 82,86,89,92,95,98,103,106,109,112,116,119,122,125,129,132,135,139,

%U 142,146,149,152,155,159,162,165,168,173,176,179,182,185,189,192,195,198,202,206,209,212,216,219,222,225,228,232,235,238,242,246,249,252,255,259,262,265,268,271,276,279,282,285,289,292,295,298,302,305,309,312,315,319,322,325,328,332,335,338,341,346,349,352,355,358,362,365,368,371,375,379,382,385,389,392,395,398

%N n+floor(nr/t)+floor(ns/t), where r=2^(1/2), s=2^(1/3), t=2^(1/5).

%C The sequences A184904, A184905, A184906, partition the positive integers:

%C A184904: 1,4,7,10,13,15,18,21,24,26,...

%C A184905: 2,5,8,11,14,17,20,23,27,30,...

%C A184906: 3,6,9,12,16,19,22,25,29,32,...

%C See A184812.

%t r=2^(1/2); s=2^(1/3); t=2^(1/5);

%t a[n_]:=n+Floor[n*s/r]+Floor[n*t/r];

%t b[n_]:=n+Floor[n*r/s]+Floor[n*t/s];

%t c[n_]:=n+Floor[n*r/t]+Floor[n*s/t];

%t Table[a[n],{n,1,120}] (* A184904 *)

%t Table[b[n],{n,1,120}] (* A184905 *)

%t Table[c[n],{n,1,120}] (* A184906 *)

%Y Cf. A184812, A184904, A184905.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 25 2011