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A329443 a(n) is the GCD of the binary representation of n interpreted in any numeric base.

%I A329443 #11 Nov 15 2019 21:17:00
%S A329443 0,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,1,1,
%T A329443 2,1,2,1,1,1,2,1,3,1,1,1,2,1,2,1,1,1,1,1,2,1,1,1,2,1,4,1,1,1,1,1,2,1,
%U A329443 2,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,2
%N A329443 a(n) is the GCD of the binary representation of n interpreted in any numeric base.
%H A329443 Rémy Sigrist, <a href="/A329443/b329443.txt">Table of n, a(n) for n = 0..10000</a>
%F A329443 k divides a(A329000(k)) for any k > 0.
%e A329443 For n = 42:
%e A329443 - the binary representation of 42 is "101010",
%e A329443 - the corresponding interpretations in the first bases b, alongside their GCD, are:
%e A329443   b   b+b^3+b^5  GCD
%e A329443   --  ---------  ---
%e A329443    2         42   42
%e A329443    3        273   21
%e A329443    4       1092   21
%e A329443    5       3255   21
%e A329443    6       7998    3
%e A329443 - as b + b^3 + b^5 is always divisible by 3, we have a(42) = 3.
%o A329443 (PARI) a(n) = my (g=n, d=binary(n)); for (b=3, oo, g = gcd(g, fromdigits(d,b)); if (g < b, return (g)))
%Y A329443 Cf. A329000, A329126.
%K A329443 nonn,base
%O A329443 0,7
%A A329443 _Rémy Sigrist_, Nov 13 2019