All numbers in base 10 with one digit {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} are palindromic ones. The number of palindromic numbers with two digits is 9:
10^{1}  10^{2}  10^{3}  10^{4}  10^{5}  10^{6}  10^{7}  10^{8}  10^{9}  10^{10}  
n natural  9  90  199  1099  1999  10999  19999  109999  199999  
n even  5  9  49  89  489  +  +  +  +  + 
n odd  5  10  60  110  610  +  +  +  +  + 
n perfect square  3  6  13  14  19  +  +  
n prime  4  5  20  113  781  5953  
n squarefree  6  12  67  120  675  +  +  +  +  + 
n nonsquarefree (μ(n)=0)  3  6  41  78  423  +  +  +  +  + 
n square with prime root  2  3  5  
n with an even number of distinct prime factors[?] (μ(n)=1)  2  6  35  56  324  +  +  +  +  + 
n with an odd number of distinct prime factors (μ(n)=1)  5  7  33  65  352  +  +  +  +  + 
n even with an odd number of prime factors  
n even with ann odd number of distinct prime factors  1  2  9  21  100  +  +  +  +  + 
n odd with an odd number of prime factors  0  1  12  37  204  +  +  +  +  + 
n odd with an odd number of distinct prime factors  0  0  4  24  139  +  +  +  +  + 
n even squarefree with an even number of distinct prime factors  1  2  11  15  98  +  +  +  +  + 
n odd squarefree with an even number of distinct prime factors  1  4  24  41  226  +  +  +  +  + 
n odd with exactly 2 prime factors  1  4  25  39  205  +  +  +  +  + 
n even with exactly 2 prime factors  2  3  11  64  +  +  +  +  +  
n even with exactly 3 prime factors  1  3  14  24  122  +  +  +  +  + 
n even with exactly 3 distinct prime factors  
n odd with exactly 3 prime factors  0  1  12  34  173  +  +  +  +  + 
n Carmichael number  0  0  0  0  0  1+  +  +  +  + 
n for which σ(n) is palindromic  6  10  47  114  688  +  +  +  +  + 
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