I have a series of inputs and outputs from a function. Inputs are -100 to +100, with the middle value as 0.
The graph generated is quite distinctive:
But I cannot work out what mathematical pattern it seems to represent. This is the raw data as [input, output] : $$\begin{array}{r|r} -100 & 4 \\ -99 & 1 \\ -98 & 2 \\ -97 & 1 \\ -96 & 32 \\ -95 & 1 \\ -94 & 2 \\ -93 & 1 \\ -92 & 4 \\ -91 & 1 \\ -90 & 2 \\ -89 & 1 \\ -88 & 8 \\ -87 & 1 \\ -86 & 2 \\ -85 & 1 \\ -84 & 4 \\ -83 & 1 \\ -82 & 2 \\ -81 & 1 \\ -80 & 16 \\ -79 & 1 \\ -78 & 2 \\ -77 & 1 \\ -76 & 4 \\ -75 & 1 \\ -74 & 2 \\ -73 & 1 \\ -72 & 8 \\ -71 & 1 \\ -70 & 2 \\ -69 & 1 \\ -68 & 4 \\ -67 & 1 \\ -66 & 2 \\ -65 & 1 \\ -64 & 64 \\ -63 & 1 \\ -62 & 2 \\ -61 & 1 \\ -60 & 4 \\ -59 & 1 \\ -58 & 2 \\ -57 & 1 \\ -56 & 8 \\ -55 & 1 \\ -54 & 2 \\ -53 & 1 \\ -52 & 4 \\ -51 & 1 \\ -50 & 2 \\ -49 & 1 \\ -48 & 16 \\ -47 & 1 \\ -46 & 2 \\ -45 & 1 \\ -44 & 4 \\ -43 & 1 \\ -42 & 2 \\ -41 & 1 \\ -40 & 8 \\ -39 & 1 \\ -38 & 2 \\ -37 & 1 \\ -36 & 4 \\ -35 & 1 \\ -34 & 2 \\ -33 & 1 \\ -32 & 32 \\ -31 & 1 \\ -30 & 2 \\ -29 & 1 \\ -28 & 4 \\ -27 & 1 \\ -26 & 2 \\ -25 & 1 \\ -24 & 8 \\ -23 & 1 \\ -22 & 2 \\ -21 & 1 \\ -20 & 4 \\ -19 & 1 \\ -18 & 2 \\ -17 & 1 \\ -16 & 16 \\ -15 & 1 \\ -14 & 2 \\ -13 & 1 \\ -12 & 4 \\ -11 & 1 \\ -10 & 2 \\ -9 & 1\\ -8 & 8\\ -7 & 1\\ -6 & 2\\ -5 & 1\\ -4 & 4\\ -3 & 1\\ -2 & 2\\ -1 & 1\\ 0 & 0\\ 1 & 1\\ 2 & 2\\ 3 & 1\\ 4 & 4\\ 5 & 1\\ 6 & 2\\ 7 & 1\\ 8 & 8\\ 9 & 1\\ 10 & 2\\ 11 & 1\\ 12 & 4\\ 13 & 1\\ 14 & 2\\ 15 & 1\\ 16 & 16\\ 17 & 1\\ 18 & 2\\ 19 & 1\\ 20 & 4\\ 21 & 1\\ 22 & 2\\ 23 & 1\\ 24 & 8\\ 25 & 1\\ 26 & 2\\ 27 & 1\\ 28 & 4\\ 29 & 1\\ 30 & 2\\ 31 & 1\\ 32 & 32\\ 33 & 1\\ 34 & 2\\ 35 & 1\\ 36 & 4\\ 37 & 1\\ 38 & 2\\ 39 & 1\\ 40 & 8\\ 41 & 1\\ 42 & 2\\ 43 & 1\\ 44 & 4\\ 45 & 1\\ 46 & 2\\ 47 & 1\\ 48 & 16\\ 49 & 1\\ 50 & 2\\ 51 & 1\\ 52 & 4\\ 53 & 1\\ 54 & 2\\ 55 & 1\\ 56 & 8\\ 57 & 1\\ 58 & 2\\ 59 & 1\\ 60 & 4\\ 61 & 1\\ 62 & 2\\ 63 & 1\\ 64 & 64\\ 65 & 1\\ 66 & 2\\ 67 & 1\\ 68 & 4\\ 69 & 1\\ 70 & 2\\ 71 & 1\\ 72 & 8\\ 73 & 1\\ 74 & 2\\ 75 & 1\\ 76 & 4\\ 77 & 1\\ 78 & 2\\ 79 & 1\\ 80 & 16\\ 81 & 1\\ 82 & 2\\ 83 & 1\\ 84 & 4\\ 85 & 1\\ 86 & 2\\ 87 & 1\\ 88 & 8\\ 89 & 1\\ 90 & 2\\ 91 & 1\\ 92 & 4\\ 93 & 1\\ 94 & 2\\ 95 & 1\\ 96 & 32\\ 97 & 1\\ 98 & 2\\ 99 & 1\\ 100 & 4 \end{array} $$
Recall that powers of $2$ are $1,2,4,8,16,32,64,...$
This function is the largest power of $2$ dividing $n$.
For example,
$f(24)=8$ because $24$ is divisible by $8$ and is not divisble by $16$.