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#' Perfect numbers
#'
#' Under OEIS \href{https://oeis.org/A000396}{A000396}, a \emph{Perfect} number is
#' a number whose proper divisors sum up to the extent equal to the number itself. First
#' 6 abundant numbers are 6, 28, 496, 8128, 33550336, 8589869056.
#'
#' @param n the number of first \code{n} entries from the sequence.
#' @param gmp a logical; \code{TRUE} to use large number representation, \code{FALSE} otherwise.
#'
#' @return a vector of length \code{n} containing first entries from the sequence.
#'
#' @examples
#' \dontrun{
#' ## generate first 7 Perfect numbers
#' print(Perfect(10))
#' }
#'
#' @seealso \code{\link{Deficient}}, \code{\link{Abundant}}
#' @rdname A000396
#' @aliases A000396
#' @export
Perfect <- function(n, gmp=TRUE){
## Preprocessing for 'n'
n = check_n(n)
## Main Computation : first, compute in Rmpfr form
output = as.bigz(numeric(n))
first10 = as.bigz(c("6", "28", "496", "8128", "33550336", "8589869056", "137438691328", "2305843008139952128", "2658455991569831744654692615953842176", "191561942608236107294793378084303638130997321548169216"))
if (n<=10){
output = first10[1:n]
} else {
output[1:10] = first10
iter = 10
tgt = as.bigz("191561942608236107294793378084303638130997321548169216")
while (iter < n){
tgt = tgt + 1
if (sum(gmp_divisors_proper(tgt))==tgt){
iter = as.integer(iter + 1)
output[iter] = tgt
}
}
}
## gmp
if (!gmp){
output = as.integer(output)
}
return(output)
}
#' @keywords internal
#' @noRd
is.Perfect <- function(tgt){
pdivs = gmp_divisors_proper(tgt)
if (sum(pdivs)==tgt){
return(TRUE)
} else {
return(FALSE)
}
}
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