Let N denote the number of all natural numbers n such that n is divisible by a prime p> n and p < 20 . What is the value of N ?

Step-by-step solution

Since P > n and P >20 Hence for the times from 2 to 20 we calculate possibilities that that n < P ^2 ( array |c|l| Prime No. & Natural Number n 2 & 2 3 & 3,6 5 & 5,10,15,20 7 & 7,14,21,28,35,42 11 & 11,22,33,44,55,66,77,88,99,110 13 & 13,26,39,52,65,78,91,104,117,130,143,156 17 & 17,34,51,68,85,102,119,136,153,170, & 187,204,221,238,255,272 19 & 19,38,57,76,95,114,133,152,171,190, & 209,228,247,266,285,304,323,342 array ) Total numbers = 69