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GCD of the set of positions of 1's in the reversed binary expansion of n.
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%I #16 Nov 15 2022 15:06:35

%S 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 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 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

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

%C a(n) is even if and only if n is in A062880. - _Robert Israel_, Oct 13 2020

%H Robert Israel, <a href="/A326674/b326674.txt">Table of n, a(n) for n = 1..10000</a>

%F Trivially, a(n) <= log_2(n). - _Charles R Greathouse IV_, Nov 15 2022

%e 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 f:= proc(n) local B;

%p B:= convert(n,base,2);

%p igcd(op(select(t -> B[t]=1, [$1..ilog2(n)+1])))

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Oct 13 2020

%t Table[GCD@@Join@@Position[Reverse[IntegerDigits[n,2]],1],{n,100}]

%Y Positions of 1's are A291166, and non-1's are A291165.

%Y GCDs of prime indices are A289508.

%Y GCDs of strict partitions encoded by FDH numbers are A319826.

%Y Numbers whose binary positions are pairwise coprime are A326675.

%Y Cf. A000120, A051293, A062880, A070939, A326667, A326668, A326669, A326670, A326672, A326673.

%K nonn,base

%O 1,2

%A _Gus Wiseman_, Jul 17 2019