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A371289
Numbers whose binary indices have squarefree product.
5
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
OFFSET
1,3
COMMENTS
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.
EXAMPLE
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}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SquareFreeQ[Times@@bpe[#]]&]
CROSSREFS
For prime instead of binary indices we have A302505.
For squarefree parts we have A368533, for prime indices A302478.
A005117 lists squarefree numbers.
A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
Sequence in context: A161673 A368533 A309126 * A004836 A039030 A162231
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Mar 25 2024
STATUS
approved