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%I #11 Dec 29 2020 20:37:32
%S 1,1,1,1,1,1,3,1,1,1,5,1,3,1,1,1,1,1,9,1,1,1,11,1,1,1,1,3,7,1,15,1,1,
%T 1,1,1,9,1,1,1,5,1,21,1,1,1,23,1,3,1,1,3,13,1,1,1,1,1,29,1,15,1,1,1,1,
%U 5,33,1,1,3,35,1,9,1,1,3,1,1,39,1,1,1,41,1,1,1,1,1,11,1,9,1,1,1,1,1,3,1,1,1,25,1,51,1,1
%N a(n) = gcd(n-1, A336466(n)); Odd part of A340081(n).
%H Antti Karttunen, <a href="/A340084/b340084.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A340084/a340084.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = gcd(n-1, A336466(n)).
%F a(n) = A000265(A340081(n)) = A336466(n) / A340085(n).
%F For n >= 2, a(n) = A000265(n-1) / A340086(n).
%F For n >= 1, a(A000040(n)) = A057023(n).
%F For n >= 0, a(A019565(2*n)) = A339899(n).
%t Array[GCD[#1 - 1, #2] & @@ {#, Times @@ Map[If[# <= 2, 1, (# - 1)/2^IntegerExponent[# - 1, 2]] &, Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]]]} &, 105] (* _Michael De Vlieger_, Dec 29 2020 *)
%o (PARI)
%o A000265(n) = (n>>valuation(n,2));
%o A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
%o A340084(n) = { my(u=A336466(n)); gcd(n-1, u); };
%Y Cf. A000265, A003958, A003961, A019565, A057023, A336466, A339899, A340081, A340085, A340086.
%Y Cf. also A049559.
%K nonn
%O 1,7
%A _Antti Karttunen_, Dec 29 2020
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