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A371289
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Numbers whose binary indices have squarefree product.
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5
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0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 48, 49, 64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87, 96, 97, 112, 113, 512, 513, 516, 517, 576, 577, 580, 581, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1040, 1041, 1042
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OFFSET
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1,3
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COMMENTS
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A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
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LINKS
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EXAMPLE
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The terms together with their binary expansions and binary indices begin:
0: 0 ~ {}
1: 1 ~ {1}
2: 10 ~ {2}
3: 11 ~ {1,2}
4: 100 ~ {3}
5: 101 ~ {1,3}
6: 110 ~ {2,3}
7: 111 ~ {1,2,3}
16: 10000 ~ {5}
17: 10001 ~ {1,5}
18: 10010 ~ {2,5}
19: 10011 ~ {1,2,5}
20: 10100 ~ {3,5}
21: 10101 ~ {1,3,5}
22: 10110 ~ {2,3,5}
23: 10111 ~ {1,2,3,5}
32: 100000 ~ {6}
33: 100001 ~ {1,6}
48: 110000 ~ {5,6}
49: 110001 ~ {1,5,6}
64: 1000000 ~ {7}
65: 1000001 ~ {1,7}
66: 1000010 ~ {2,7}
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MATHEMATICA
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bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SquareFreeQ[Times@@bpe[#]]&]
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CROSSREFS
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For prime instead of binary indices we have A302505.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
Cf. A325118, A326782, A371290, A371291, A371292, A371293, A371443, A371446, A371448, A371449, A371452, A371453.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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