A palindromic number is a symmetrical number written in some base a as a_{1}a_{2}a_{3} ...|... a_{3}a_{2}a_{1}.
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 square-free | 6 | 12 | 67 | 120 | 675 | + | + | + | + | + |
n non-square-free (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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