which n <= 20 can be constructed a regular n-gonwith compass and straightedge? return all the possible numbers in a list
Relevant Theorem: The Gauss-Wantzel theorem, also known as the Gauss-Wantzel-Steiner theorem, is a result in geometry that provides a necessary and sufficient condition for a polygon to be constructible using only a compass and straightedge. This theorem is named after the mathematicians Carl Friedrich Gauss, Johann Jakob Steiner, and Pierre Wantzel.

The theorem states that a regular polygon with n sides can be constructed using only a compass and straightedge if and only if n is the product of a power of 2 and any number of distinct Fermat primes. A Fermat prime is a prime number that can be expressed in the form 2^(2^k) + 1, where k is a non-negative integer.

For example, a regular polygon with 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 272, 320, 340, 384, 408, 480, 510, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 1024, 1028, 1088, 1280, 1360, 1536, 1632, 1920, 2040, 2048, 2056, 2176, 2560, 2720, 3072, 3264, 3840, 4080, 4096, 4112, 4352, 5120, 5440, 6144, 6528, 7680, 8160, 8192, 8224, 8704, 10240, 10880, 12288, 13056, 15360, 16320, 16384, 16448, 17408, 20480, 21760, 24576, 26112, 30720, 32640, 32768, 32896, 34816, 40960, 43520, 49152, 52224, 61440, 65280, 65536, 65692, 69632, 81920, 87040, 98304, 104448, 122880, 130560, 131072, 131184, 139264, 163840, 174080, 196608, 208896, 245760, 261120, 262144, 262288, 278528, 327680, 348160, 393216, 417792, 491520, 522240, 524288, 524576, 557056, 655360, 696320, 786432, 835584, 983040, 1044480, 1048576, 1049088, 1114112, 1310720, 1392640, 1572864, 1671168, 1966080, 2088960, 2097152, 2098176, 2228224, 2621440, 2785280, 3145728, 3342336, 3932160, 4177920, 4194304, 4196352, 4456448, 5242880, 5570560, 6291456, 6684672, 7864320, 8355840, 8388608, 8392704, 8912896, 10485760, 11141120, 12582912, 13369344, 15728640, 16711680, 16777216, 16785408, 17825792, 20971520, 22282240, 25165824, 26738688, 31457280, 33423360, 33554432, 33570816, 35651584, 41943040, 44564480, 50331648, 53477376, 62914560, 66846720, 67108864, 67141632, 71303168, 83886080, 89128960, 100663296, 106954752, 125829120, 133693440, 134217728, 134283264, 142606336, 167772160, 178257920, 201326592, 213909504, 251658240, 
나침반과 직선 자를 사용하여 어떤 n <= 20의 정나선을 만들 수 있습니까? 목록에서 가능한 모든 숫자를 반환합니다.
관련 정리: 가우스-반첼-슈타이너 정리라고도 알려진 가우스-반첼 정리는 나침반과 직선자만으로 다각형을 구성할 수 있는 필요충분조건을 제공하는 기하학의 결과입니다. 이 정리는 수학자 칼 프리드리히 가우스, 요한 야콥 슈타이너, 피에르 만첼의 이름을 따서 명명되었습니다.

이 정리에 따르면 n이 2의 거듭제곱과 임의의 수의 고유한 페르마 소수의 곱인 경우에만 나침반과 직선자만 사용하여 n개의 변을 가진 정다각형을 만들 수 있다는 것입니다. 페르마 소수는 2^(2^k) + 1 형식으로 표현할 수 있는 소수로, 여기서 k는 음이 아닌 정수입니다.

예를 들어, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 64, 68, 80, 85, 96, 102, 120, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 272, 320의 정다각형이 있습니다, 340, 384, 408, 480, 510, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 1024, 1028, 1088, 1280, 1360, 1536, 1632, 1920, 2040, 2048, 2056, 2176, 2560, 2720, 3072, 3264, 3840, 4080, 4096, 4112, 4352, 5120, 5440, 6144, 6528, 7680, 8160, 8192, 8224, 8704, 10240, 10880, 12288, 13056, 15360, 16320, 16384, 16448, 17408, 20480, 21760, 24576, 26112, 30720, 32640, 32768, 32896, 34816, 40960, 43520, 49152, 52224, 61440, 65280, 65536, 65692, 69632, 81920, 87040, 98304, 104448, 122880, 130560, 131072, 131184, 139264, 163840, 174080, 196608, 208896, 245760, 261120, 262144, 262288, 278528, 327680, 348160, 393216, 417792, 491520, 522240, 524288, 524576, 557056, 655360, 696320, 786432, 835584, 983040, 1044480, 1048576, 1049088, 1114112, 1310720, 1392640, 1572864, 1671168, 1966080, 2088960, 2097152, 2098176, 2228224, 2621440, 2785280, 3145728, 3342336, 3932160, 4177920, 4194304, 4196352, 4456448, 5242880, 5570560, 6291456, 6684672, 7864320, 8355840, 8388608, 8392704, 8912896, 10485760, 11141120, 12582912, 13369344, 15728640, 16711680, 16777216, 16785408, 17825792, 20971520, 22282240, 25165824, 26738688, 31457280, 33423360, 33554432, 33570816, 35651584, 41943040, 44564480, 50331648, 53477376, 62914560, 66846720, 67108864, 67141632, 71303168, 83886080, 89128960, 100663296, 106954752, 125829120, 133693440, 134217728, 134283264, 142606336, 167772160, 178257920, 201326592, 213909504, 251658240,