How many positive integers n <= 20 000 have the properties that 2n has 64 positive divisors including 1 and 2n, and 5n has 60 positive divisors including 1 and 5n?

Guest Feb 23, 2021

#1**0 **

60 divisors:

5040 ,7920, 8400 ,9360 ,10800 ,11088 ,11340, 11760 ,12240 ,12960 ,13104 ,13680 ,15600, 16200, 16560 ,17136 ,17820 ,18000 ,18144, 19152 ,19440>>Total of 21 integers.

Note: for some reason, they want you to express the number as "5n", which means every number divisible by 5 has to be expressed as "5n". Example: 5040 / 5==1008. Any number that is not evenly divisible by 5, you simply ignore it, I assume.

64 divisors:

7560, 9240, 10920, 11880, 13440, 14040, 14280, 15960, 16632, 17160, 17280, 18360, 19320, 19656>>Total of 14 integers.

Note: Similarly here, except they want you to express it as "2n", which includes all 14 integers.

Guest Feb 23, 2021

edited by
Guest
Feb 23, 2021