Question

For how many odd positive integers n<1000 does the number of positive divisors of n divide n?

Answer 1

can we look at a simpler example, n < 10

Answer 2

for n<10 we have 1,3,5,7,9 . 1 has 1 positive divisor and 1 divides 1. 3 has 2 positive divisor and that doesnt divide 3.
5 has 2 , 7 has 2 ( in general every prime number has 2 positive divisors)
9 has three positive divisors, and that divides 3
so for n<10 , we have 2 numbers

Answer 3

this looks like a pretty complicated problem. maybe you could program a computer to do it , thats what i would do

Answer 4

ok, thank! (:

Answer 5

ok i've got the answer ^^

Answer 6

how did you get it ?

Answer 7

i use my brain :D

Answer 8

no no, it takes too long that way

Answer 9

you can exclude prime numbers,

Answer 10

yes, i got the solution of that problem

Answer 11

it's become easy when i knew the max value of "the number of positive divisors" is 10 :D

Answer 12

wait what?

Answer 13

sorry i didnt follow