Using manual calculation, I get following results:

106 for each group.

This appears much smaller than your results.

Using pwr package in R and calculating sample size for t-tests, as described here, I get following result:

library(pwr)
pwr.t.test(n = , d = 0.389, sig.level = 0.05 , power = 0.8, type = "two.sample") 

Output:

 Two-sample t test power calculation 

          n = 104.707      <<<<<<<<< NOTE
          d = 0.389
  sig.level = 0.05
      power = 0.8
alternative = two.sided

NOTE: n is number in *each* group

Here, sample size of 105 is much smaller than your results.

Effect size used above was calculated as follows:

d (effect size) = (diff between means)/pooledSD
(diff between means) = 54.6 - 36.8 = 17.8
pooledSD = sqrt((sd1^2 + sd2^2)/2) : 45.7
d = 17.8/45.7 = 0.389