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A372683
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Least squarefree number >= 2^n.
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17
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1, 2, 5, 10, 17, 33, 65, 129, 257, 514, 1027, 2049, 4097, 8193, 16385, 32770, 65537, 131073, 262145, 524289, 1048577, 2097154, 4194305, 8388609, 16777217, 33554433, 67108865, 134217730, 268435457, 536870913, 1073741826, 2147483649, 4294967297, 8589934594
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their binary expansions and binary indices begin:
1: 1 ~ {1}
2: 10 ~ {2}
5: 101 ~ {1,3}
10: 1010 ~ {2,4}
17: 10001 ~ {1,5}
33: 100001 ~ {1,6}
65: 1000001 ~ {1,7}
129: 10000001 ~ {1,8}
257: 100000001 ~ {1,9}
514: 1000000010 ~ {2,10}
1027: 10000000011 ~ {1,2,11}
2049: 100000000001 ~ {1,12}
4097: 1000000000001 ~ {1,13}
8193: 10000000000001 ~ {1,14}
16385: 100000000000001 ~ {1,15}
32770: 1000000000000010 ~ {2,16}
65537: 10000000000000001 ~ {1,17}
131073: 100000000000000001 ~ {1,18}
262145: 1000000000000000001 ~ {1,19}
524289: 10000000000000000001 ~ {1,20}
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MATHEMATICA
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Table[NestWhile[#+1&, 2^n, !SquareFreeQ[#]&], {n, 0, 10}]
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PROG
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(PARI) a(n) = my(k=2^n); while (!issquarefree(k), k++); k; \\ Michel Marcus, May 29 2024
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CROSSREFS
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The opposite (greatest squarefree number <= 2^n) is A372889.
The difference from 2^n is A373125.
For prime instead of squarefree we have:
A000120 counts ones in binary expansion (binary weight), zeros A080791.
A061398 counts squarefree numbers between primes (exclusive).
A077643 counts squarefree terms between powers of 2, run-lengths of A372475.
A143658 counts squarefree numbers up to 2^n.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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