with(combinat);

R :=
proc(n)
    local bits, len, part, cert,
    blocks, pos, offs, val, seg;

    bits := convert(n, base, 2);
    len := nops(bits);

    for part in partition(len) do
        blocks := [];

        pos := len;
        for seg in part do
            offs := pos-seg+1;

            if bits[pos] > 0 then
                val :=  add(bits[q]*2^(q-offs), q=offs..pos);
            else
                break;
            fi;

            blocks := [op(blocks), val];
            pos := pos-seg;
        od;

        if nops(blocks) = nops(part) then
            for pos to nops(blocks)-1 do
                if blocks[pos+1] mod blocks[pos] > 0 then
                    break;
                fi;
            od;

            if pos = nops(blocks) then
                cert := [part, blocks];
                break;
            fi;
        fi;
    od;

    cert;
end;

X := n -> nops(op(1, R(n)));