N is a natural number. We call N the product of non-zero numbers as the "index number" of N. For example, the index number of 1 is 1, and the index number of 27 is 2*7=14.40. The index number is 4, then it is 1~99, What is the sum of the indices of these ninety-nine natural numbers?
N是自然数，我们称N是非零数字的乘积为N的"指标数"，如1的指标数为1，27的指标数为2*7=14.40的指标数是4，则在1～99，这九十九个自然数的指标数的和是多少．
<gadget id="calculator">1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9</gadget>
<output>45</output>

<gadget id="calculator">1 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9</gadget>
<output>46</output>

<gadget id="calculator">45 * 46</gadget>
<output>2_070</output>

<gadget id="calculator">45 + 2_070</gadget>
<output>2_115</output>

<result>2_115</result>