Вы были почти там, см. Комментарии:
alpha = c(0.01,0.05,0.10,0.20)
beta = c(0.50,0.60,0.70,0.80,0.90)
# nrow and ncol depends on the length of alpha and beta
pwrmx <- matrix(data=NA, nrow=length(alpha), ncol=length(beta))
# iterate over the length so that you can use it to assign back at the correct index in matrix
for (i in 1:length(alpha)){
for (j in 1:length(beta)){
# as you are interested in the number n from the power analysis
pwrmx[i,j] <- (power.prop.test(n=NULL, p1=0.25, p2=0.4, sig.level = alpha[i], power = beta[j]))$n
}
}
pwrmx
# . [,1] [,2] [,3] [,4] [,5]
#[1,] 129.38048 155.72219 186.60552 226.29474 287.6656
#[2,] 74.90845 95.24355 119.70057 151.86886 202.8095
#[3,] 52.75810 70.01993 91.18885 119.50901 165.1130
#[4,] 32.02629 45.74482 63.12283 87.00637 126.4575