What is the purpose of b <-c() in this code? - r

Question

I have written a code to find a positive integer that has more divisors than any smaller positive integer has. My code is right but I noticed that I wrote a step only because I had solved other questions similarly but I don't really understand the intuition of why we write this particular line:
b <- c()
Also, why is there a "b" in c(b, sum..) as in the below line:
b <- c(b, sum(p %% c(1:p) == 0))
Here is the full code:
code <- function(n) {
if (n < 1 | n %% 1 != 0)
print("Only positive integers allowed")
else if (n <= 2)
return(TRUE)
else {
a <- sum(n %% c(1:n) == 0)
b <- c()
for (p in 1:(n-1)) {
b <- c(b, sum(p %% c(1:p) == 0))
}
return(max(b) < a)
}
}
code(8)
code(6)
code(-7)

Answer 1

As already explained in comments the purpose of b<-c() is to initialise an empty vector and fill it in the loop. Also the reason why you are using b <- c(b,sum(p%%c(1:p)== 0)) is to append new values to already existing values of b.
For example,
b <- c()
b
#NULL
b <- c(b, 1)
b
#[1] 1
b <- c(b, 2)
b
#[1] 1 2
Usually, it is not a good practice to grow an object in a loop, it is highly inefficient to do that. If the size of output is fixed you can initialise a vector with fixed size and then fill it in the loop.
code <- function(n){
if (n<1 | n%%1!=0)
print("Only positive integers allowed")
else if (n <= 2)
return(TRUE)
else{
a <- sum(n%%c(1:n) == 0)
b <- integer(n-1) #Creates a vector with 0's of length n-1
for (p in 1:(n-1)) {
b[p] <- sum(p%%c(1:p)== 0)
}
return(max(b) < a)
}
}
Or in this case you can save only the max value of b since all other values are not important.
code <- function(n){
if (n<1 | n%%1!=0)
print("Only positive integers allowed")
else if (n <= 2)
return(TRUE)
else{
a <- sum(n%%c(1:n) == 0)
max_b <- 0
for (p in 1:(n-1)) {
val <- sum(p%%c(1:p)== 0)
if(val > max_b) max_b <- val
}
return(max_b < a)
}
}