The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#39?  Pick.
A) 17 B) 18 C) 19 D) 20 E) 21
First, let's translate the expression 21#39, using the definition given:   21#39 = 21×24×27×30×33×36×39   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#39 = 3^7(7×8×9×10×11×12×13)   Now let's replace each consecutive integer with its prime factorization:   21#39 = 3^7(7×2^3×3^2×(2×5)×11×(2^2×3)×13)   Let's group the prime bases:   21#39 = 2^6×3^10×5×7×11×13   The sum of the exponents is  6 + 10 + 1 + 1 + 1 + 1= 
<gadget id="calculator"> 6 + 10 + 1 + 1 + 1 + 1</gadget>
<output>20</output>
20   The answer is 20.
<result>D</result>
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#39?