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A328671
Numbers whose binary indices are relatively prime and pairwise indivisible.
8
1, 6, 12, 18, 20, 22, 24, 28, 48, 56, 66, 68, 70, 72, 76, 80, 82, 84, 86, 88, 92, 96, 104, 112, 120, 132, 144, 148, 176, 192, 196, 208, 212, 224, 240, 258, 264, 272, 274, 280, 296, 304, 312, 320, 322, 328, 336, 338, 344, 352, 360, 368, 376, 384, 400, 416, 432
OFFSET
1,2
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.
FORMULA
Intersection of A291166 with A326704.
EXAMPLE
The sequence of terms together with their binary expansions and binary indices begins:
1: 1 ~ {1}
6: 110 ~ {2,3}
12: 1100 ~ {3,4}
18: 10010 ~ {2,5}
20: 10100 ~ {3,5}
22: 10110 ~ {2,3,5}
24: 11000 ~ {4,5}
28: 11100 ~ {3,4,5}
48: 110000 ~ {5,6}
56: 111000 ~ {4,5,6}
66: 1000010 ~ {2,7}
68: 1000100 ~ {3,7}
70: 1000110 ~ {2,3,7}
72: 1001000 ~ {4,7}
76: 1001100 ~ {3,4,7}
80: 1010000 ~ {5,7}
82: 1010010 ~ {2,5,7}
84: 1010100 ~ {3,5,7}
86: 1010110 ~ {2,3,5,7}
88: 1011000 ~ {4,5,7}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Select[Range[100], GCD@@bpe[#]==1&&stableQ[bpe[#], Divisible]&]
CROSSREFS
The version for prime indices (instead of binary indices) is A328677.
Numbers whose binary indices are relatively prime are A291166.
Numbers whose distinct prime indices are pairwise indivisible are A316476.
BII-numbers of antichains are A326704.
Relatively prime partitions whose distinct parts are pairwise indivisible are A328676, with strict case A328678.
Sequence in context: A105935 A105289 A328608 * A051774 A119357 A097216
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 29 2019
STATUS
approved