R's AIC values differ from published values

Using the Cement hardening data in Anderson (2008) Model Based Inference in
the Life Sciences. A Primer on Evidence, and working with the best model
which is
? ?lm ?( ?y ?~ ? x1 ? + ? x2, ? ?data = cement ?)
the AIC value from R is

? ?model ? ?<- ? ?lm ?( formula ? = ? y ? ~ ? x1 ? + ?x2 ?, ? data =
cement ?)
? ?AIC ( model )

64.312

which can be converted to AICc by adding the bias correction factor
2*K*(K+1)/(n-K-1) to give the AICc value of
69.312
(addition of 5, where n=13 and K=4).

This same value, 69.31, can be obtained using R package
AICcmodavg

? library ?( ?AICcmodavg ?)
? data (cement)
? cement
? Cand.models ? <- ? list( )
? Cand.models[[1]] ? <- ? lm ?( ?y ?~ ? x1 ? + ? x2, ? ?data = cement ?)
? Cand.models[[2]] ? <- ? lm ?( ?y ? ?~ ? x3 ? + ? x4, ? ? data = cement ?)
? Cand.models[[3]] ? <- ? lm ?( ?y ? ~ ? x1 + x2 + x1 * x2, ? data =
cement ?)
? Cand.models[[4]] ? <- ? lm ?( ?y ? ~ ? x3 ?+ ?x4 ?+ ?x3 * x4, ? data =
cement ?)
? ? ## ? vector of model names
? Modnames ? <- ? paste("MODEL", 1:4, sep=" ? ? ")
? ? ## ? AICc
? aictab ? ( ?cand.set ? = ? Cand.models, ? modnames ?= ?Modnames ?)

However, the AICc value reported by Anderson (2008) is
32.41.
The AICc value obtained using RSS value (i.e., calculating AICc "manually"
from the output of linear regression) is
32.41.

Thanks for any help.
David
New R user, minimal familiarity with statistics.

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