A328671 Numbers whose binary indices are relatively prime and pairwise indivisible.

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

Author

Gus Wiseman, Oct 29 2019

Keywords

• nonn

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.

Examples

			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}
		

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.

Cf. A000120, A121016, A285573, A303362, A304713, A305148, A316468, A316475.

Programs

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]&]

Formula

Intersection of A291166 with A326704.