cp's OEIS Frontend

A371289 Numbers whose binary indices have squarefree product.

%I A371289 #11 Mar 28 2024 11:58:01
%S A371289 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,
%T A371289 69,70,71,80,81,82,83,84,85,86,87,96,97,112,113,512,513,516,517,576,
%U A371289 577,580,581,1024,1025,1026,1027,1028,1029,1030,1031,1040,1041,1042
%N A371289 Numbers whose binary indices have squarefree product.
%C A371289 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.
%e A371289 The terms together with their binary expansions and binary indices begin:
%e A371289      0:              0 ~ {}
%e A371289      1:              1 ~ {1}
%e A371289      2:             10 ~ {2}
%e A371289      3:             11 ~ {1,2}
%e A371289      4:            100 ~ {3}
%e A371289      5:            101 ~ {1,3}
%e A371289      6:            110 ~ {2,3}
%e A371289      7:            111 ~ {1,2,3}
%e A371289     16:          10000 ~ {5}
%e A371289     17:          10001 ~ {1,5}
%e A371289     18:          10010 ~ {2,5}
%e A371289     19:          10011 ~ {1,2,5}
%e A371289     20:          10100 ~ {3,5}
%e A371289     21:          10101 ~ {1,3,5}
%e A371289     22:          10110 ~ {2,3,5}
%e A371289     23:          10111 ~ {1,2,3,5}
%e A371289     32:         100000 ~ {6}
%e A371289     33:         100001 ~ {1,6}
%e A371289     48:         110000 ~ {5,6}
%e A371289     49:         110001 ~ {1,5,6}
%e A371289     64:        1000000 ~ {7}
%e A371289     65:        1000001 ~ {1,7}
%e A371289     66:        1000010 ~ {2,7}
%t A371289 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A371289 Select[Range[0,100],SquareFreeQ[Times@@bpe[#]]&]
%Y A371289 For prime instead of binary indices we have A302505.
%Y A371289 For squarefree parts we have A368533, for prime indices A302478.
%Y A371289 A005117 lists squarefree numbers.
%Y A371289 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A371289 A070939 gives length of binary expansion.
%Y A371289 A096111 gives product of binary indices.
%Y A371289 Cf. A325118, A326782, A371290, A371291, A371292, A371293, A371443, A371446, A371448, A371449, A371452, A371453.
%K A371289 nonn,base
%O A371289 1,3
%A A371289 _Gus Wiseman_, Mar 25 2024