cp's OEIS Frontend

A326674 GCD of the set of positions of 1's in the reversed binary expansion of n.

%I A326674 #16 Nov 15 2022 15:06:35
%S A326674 1,2,1,3,1,1,1,4,1,2,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6,1,2,
%T A326674 1,3,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,
%U A326674 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A326674 GCD of the set of positions of 1's in the reversed binary expansion of n.
%C A326674 a(n) is even if and only if n is in A062880. - _Robert Israel_, Oct 13 2020
%H A326674 Robert Israel, <a href="/A326674/b326674.txt">Table of n, a(n) for n = 1..10000</a>
%F A326674 Trivially, a(n) <= log_2(n). - _Charles R Greathouse IV_, Nov 15 2022
%e A326674 The reversed binary expansion of 40 is (0,0,0,1,0,1), with positions of 1's being {4,6}, so a(40) = GCD(4,6) = 2.
%p A326674 f:= proc(n) local B;
%p A326674   B:= convert(n,base,2);
%p A326674   igcd(op(select(t -> B[t]=1, [$1..ilog2(n)+1])))
%p A326674 end proc:
%p A326674 map(f, [$1..100]); # _Robert Israel_, Oct 13 2020
%t A326674 Table[GCD@@Join@@Position[Reverse[IntegerDigits[n,2]],1],{n,100}]
%Y A326674 Positions of 1's are A291166, and non-1's are A291165.
%Y A326674 GCDs of prime indices are A289508.
%Y A326674 GCDs of strict partitions encoded by FDH numbers are A319826.
%Y A326674 Numbers whose binary positions are pairwise coprime are A326675.
%Y A326674 Cf. A000120, A051293, A062880, A070939, A326667, A326668, A326669, A326670, A326672, A326673.
%K A326674 nonn,base
%O A326674 1,2
%A A326674 _Gus Wiseman_, Jul 17 2019