MathCounts Training – Number Theory – 6

________ What is the sum of all positive two-digit integers with exactly 12 positive factors? $$ $$
________ What is the sum of the three numbers less than 1000 that have exactly five positive integer divisors? $$ $$
________ The sequence 3, 4, 13, 15, 30, 33, 54, 58, 85, 90, …. contains, in increasing order, all the positive integers that yield a triangle number when multiplied by 7. What is the $100^{th}$ term of this sequence? $$ $$
________ How many whole numbers $n$, such that $100 \le n \le 1000$, have the same number of odd factors as even factors? $$ $$
________ How many positive integer factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $1,2,3,4,6,$ and $12$.$$ $$