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A345947 a(n) = gcd(A153151(n), A344875(n)).

%I A345947 #13 Jul 06 2021 20:06:15
%S A345947 1,3,2,7,4,1,6,15,8,3,10,1,12,1,2,31,16,1,18,1,4,3,22,1,24,1,26,3,28,
%T A345947 1,30,63,4,3,2,7,36,1,2,3,40,1,42,1,4,3,46,1,48,1,2,3,52,1,2,5,4,3,58,
%U A345947 1,60,1,2,127,16,5,66,1,4,3,70,1,72,1,2,3,4,1,78,1,80,3,82,1,4,1,2,3,88,1,18,7,4,3,2,1,96
%N A345947 a(n) = gcd(A153151(n), A344875(n)).
%H A345947 Antti Karttunen, <a href="/A345947/b345947.txt">Table of n, a(n) for n = 1..16384</a>
%F A345947 a(n) = gcd(A153151(n), A344875(n)).
%F A345947 a(n) = A344875(n) / A345948(n).
%F A345947 a(n) = A153151(n) / A345949(n).
%F A345947 a(2n-1) = A345937(2n-1), for n >= 1.
%t A345947 Array[GCD[Which[# < 2, #, IntegerQ[Log2@ #], 2 # - 1, True, # - 1], Times @@ Map[If[#1 == 2, 2^(#2 + 1) - 1, #1^#2 - 1] & @@ # &, FactorInteger[#]]] &, 97] (* _Michael De Vlieger_, Jul 06 2021 *)
%o A345947 (PARI)
%o A345947 A153151(n) = if(!n,n,if(!bitand(n,n-1),(n+n-1),(n-1)));
%o A345947 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A345947 A345947(n) = gcd(A153151(n), A344875(n));
%Y A345947 Cf. A153151, A344875, A345948, A345949.
%Y A345947 Cf. also A344877, A344969, A345937.
%K A345947 nonn
%O A345947 1,2
%A A345947 _Antti Karttunen_, Jul 01 2021