# Which one should I consider: AIC or AICc

I want to run geographically weighted regression (GWR) with 5 independent variables (the first one is of my direct interest, while four are confounders). I ran various models (with fixed bandwidth [BW]) and for and each, I received AICc and AIC. Following is the output:

       [BW]   [AICc]     [AIC]
[1,]   92 -1219.667 -1160.555
[2,]   92 -1223.569 -1166.525
[3,]   92 -1231.206 -1175.681
[4,]   92 -1234.278 -1177.220
[5,]   92 -1253.736 -1200.312
[6,]   92 -1262.010 -1208.239
[7,]   92 -1297.094 -1212.467
[8,]   92 -1297.599 -1219.058
[9,]   92 -1303.253 -1220.423
[10,]   92 -1305.397 -1223.153
[11,]   92 -1318.119 -1237.963
[12,]   92 -1342.503 -1235.855
[13,]   92 -1344.737 -1235.568
[14,]   92 -1356.322 -1243.391
[15,]   92 -1367.295 -1256.171
[16,]   92 -1387.675 -1242.861
[17,]   92 -1389.274 -1247.099
[18,]   92 -1395.720 -1255.762
[19,]   92 -1416.640 -1243.229
[20,]   92 -1417.227 -1241.243
[21,]   92 -1440.021 -1227.826


My question is, should I consider AIC or AICc to choose the better model? As you can see, smallest AICc corresponds to model # 21 and smallest AIC corresponds with model # 15 & 18. This is bothering me because model # 21 has all five variables, while model 15 has only three confounders (out of 4) and model 18 has all the confounders. In both of these last two models, I do not have main predictor variable.

$$\frac{N}{K} < 40$$
where $K$ is the total number of parameters of the likelihood and $N$ is the sample size but this is not set in stone. You should check if that makes sense for your specific problem.