Compute the sum of all positive integers k for which the number k*1984*2 has exactly 21 positive divisors.

Guest Jun 20, 2021

#1**+2 **

To find divisors, we must prime factorize the number.

1984*2 = 2^7 × 31

Using the divisor formula, however, we find that there is no integer value of k that this is true (8*2*(any integer) cannot = 21)

Because of this, there is no number that satisfies this, meaning the sum is 0

Additional material on the divisor formula I found on google is here: https://www.themathdoctors.org/counting-divisors-of-a-number/

Sidenote: If there was no extra *2, then k=31 would make the number 1984*31 have 21 divisors.

EnchantedLava68 Jun 20, 2021