##Haskell, 28 bytes

f n=sum[1|1<-gcd n<$>[1..n]] 

Uses Haskell's pattern matching of constants. The tricks here are fairly standard for golfing, but I'll explain to a general audience.

The expression gcd n<$>[1..n] maps gcd n onto [1..n]. In other words, it computes the gcd with n of each number from 1 to n:

[gcd n i|i<-[1..n]] 

From here, the desired output is the number of 1 entries, but Haskell lacks a count function. The idiomatic way to filter to keep only 1's, and take the resulting length, which is much is too long for golfing.

Instead, the filter is simulated by a list comprehension [1|1<-l] with the resulting list l. Usually, list comprehensions bind values onto variable like in [x*x|x<-l], but Haskell allows a pattern to be matched against, in this case the constant 1.

So, [1|1<-l] generating a 1 on each match of 1, effectively extracting just the 1's of the original list. Calling sum on it gives its length.

Haskell, 28 bytes

f n=sum[1|1<-gcd n<$>[1..n]] 

Uses Haskell's pattern matching of constants. The tricks here are fairly standard for golfing, but I'll explain to a general audience.

The expression gcd n<$>[1..n] maps gcd n onto [1..n]. In other words, it computes the gcd with n of each number from 1 to n:

[gcd n i|i<-[1..n]] 

From here, the desired output is the number of 1 entries, but Haskell lacks a count function. The idiomatic way to filter to keep only 1's, and take the resulting length, which is much is too long for golfing.

Instead, the filter is simulated by a list comprehension [1|1<-l] with the resulting list l. Usually, list comprehensions bind values onto variable like in [x*x|x<-l], but Haskell allows a pattern to be matched against, in this case the constant 1.

So, [1|1<-l] generating a 1 on each match of 1, effectively extracting just the 1's of the original list. Calling sum on it gives its length.

##Haskell, 28 bytes

f n=sum[1|1<-gcd n<$>[1..n]] 

Uses Haskell's pattern matching of constants. The tricks here are fairly standard for golfing, but I'll explain to a general audience.

The expression gcd n<$>[1..n] maps gcd n onto [1..n]. In other words, it computes the gcd with n of each number from 1 to n:

[gcd n i|i<-[1..n]] 

From here, the desired output is the number of 1 entries, but Haskell lacks a count function. The idiomatic way to filter to keep only 1's, and take the resulting length, which is much is too long for golfing.

Instead, the filter is simulated by a list comprehension [1|1<-l] with the resulting list l. Usually, list comprehensions bind values onto variable like in [x*x|x<-l], but Haskell allows a pattern to be matched against, in this case the constant 1.

So, [1|1<-l] generating a 1 on each match of 1, effectively extracting just the 1's of the original list. Calling sum on it gives its length.

##Haskell, 28 bytes

f n=sum[1|1<-gcd n<$>[1..n]] 

Uses Haskell's pattern matching of constants. The tricks here are fairly standard for golfing, but I'll explain to a general audience.

The expression gcd n<$>[1..n] maps gcd n onto [1..n]. In other words, it computes the gcd with n of each number from 1 to n:

[gcd n i|i<-[1..n]] 

From here, the desired output is the number of 1 entries, but Haskell lacks a count function. The idiomatic way to filter to keep only 1's, and take the resulting length, which is much is too long for golfing.

Instead, the filter is simulated by a list comprehension [1|1<-l] with the resulting list l. Usually, list comprehensions bind values onto variable like in [x*x|x<-l], but Haskell allows a pattern to be matched against, in this case the constant 1.

So, [1|1<-l] generating a 1 on each match of 1, effectively extracting just the 1's of the original list. Calling sum on it gives its length.