DynamicModule[{shapes, t, a, next, keyframes},
 shapes[i_] :=
  Thread@{Table[
     ColorData["BlueGreenYellow"]@Rescale[a, {1, i}], {a, i}],
    Disk /@ First@
      Fold[Module[{pts = #[[1]], r = #[[2]],
          n = #2}, {Join @@
           Table[# + n r Through@{Cos, Sin}[a 2 Pi/n + Pi/2] & /@
             RotationTransform[a 2 Pi/n + If[n == 2, Pi/2, 0]]@
              pts, {a, n}], n r}] &, {{{0., 0.}}, 1},
       Join @@ ConstantArray @@@ FactorInteger@i]};
 t = 1;
 a = 1;
 next[] :=
  keyframes =
   Thread[{Prepend[#, #[[1]]], #2} & @@ (shapes /@ {a, a + 1})];
 next[];
 Dynamic[If[(t += .02) >= a + 1, a++; next[]];
  Graphics[{Blend[{#[[1]], #2[[1]]}, t - a],
      Disk[#[[2, 1]] + (t - a) (#2[[2, 1]] - #[[2, 1]])]} & @@@
    keyframes, PlotRange -> t*{{-2, 2}, {-2, 2}}, AspectRatio -> 1,
   ImageSize -> 300]]]