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

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Jul 17 2019

Keywords

• nonn
• base

Comments

a(n) is even if and only if n is in A062880. - Robert Israel, Oct 13 2020

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

GCDs of prime indices are A289508.

GCDs of strict partitions encoded by FDH numbers are A319826.

Numbers whose binary positions are pairwise coprime are A326675.

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

Programs

Maple

f:= proc(n) local B;
  B:= convert(n,base,2);
  igcd(op(select(t -> B[t]=1, [$1..ilog2(n)+1])))
end proc:
map(f, [$1..100]); # Robert Israel, Oct 13 2020

Mathematica

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

Formula

Trivially, a(n) <= log_2(n). - Charles R Greathouse IV, Nov 15 2022