cp's OEIS Frontend

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

%I A328671 #5 Nov 01 2019 18:40:54
%S A328671 1,6,12,18,20,22,24,28,48,56,66,68,70,72,76,80,82,84,86,88,92,96,104,
%T A328671 112,120,132,144,148,176,192,196,208,212,224,240,258,264,272,274,280,
%U A328671 296,304,312,320,322,328,336,338,344,352,360,368,376,384,400,416,432
%N A328671 Numbers whose binary indices are relatively prime and pairwise indivisible.
%C A328671 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.
%F A328671 Intersection of A291166 with A326704.
%e A328671 The sequence of terms together with their binary expansions and binary indices begins:
%e A328671     1:         1 ~ {1}
%e A328671     6:       110 ~ {2,3}
%e A328671    12:      1100 ~ {3,4}
%e A328671    18:     10010 ~ {2,5}
%e A328671    20:     10100 ~ {3,5}
%e A328671    22:     10110 ~ {2,3,5}
%e A328671    24:     11000 ~ {4,5}
%e A328671    28:     11100 ~ {3,4,5}
%e A328671    48:    110000 ~ {5,6}
%e A328671    56:    111000 ~ {4,5,6}
%e A328671    66:   1000010 ~ {2,7}
%e A328671    68:   1000100 ~ {3,7}
%e A328671    70:   1000110 ~ {2,3,7}
%e A328671    72:   1001000 ~ {4,7}
%e A328671    76:   1001100 ~ {3,4,7}
%e A328671    80:   1010000 ~ {5,7}
%e A328671    82:   1010010 ~ {2,5,7}
%e A328671    84:   1010100 ~ {3,5,7}
%e A328671    86:   1010110 ~ {2,3,5,7}
%e A328671    88:   1011000 ~ {4,5,7}
%t A328671 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A328671 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A328671 Select[Range[100],GCD@@bpe[#]==1&&stableQ[bpe[#],Divisible]&]
%Y A328671 The version for prime indices (instead of binary indices) is A328677.
%Y A328671 Numbers whose binary indices are relatively prime are A291166.
%Y A328671 Numbers whose distinct prime indices are pairwise indivisible are A316476.
%Y A328671 BII-numbers of antichains are A326704.
%Y A328671 Relatively prime partitions whose distinct parts are pairwise indivisible are A328676, with strict case A328678.
%Y A328671 Cf. A000120, A121016, A285573, A303362, A304713, A305148, A316468, A316475.
%K A328671 nonn
%O A328671 1,2
%A A328671 _Gus Wiseman_, Oct 29 2019