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%I #6 Jan 21 2020 18:22:42
%S 1,2,1,1,1,2,1,2,3,2,1,6,1,2,1,1,1,6,1,2,1,2,1,12,1,2,3,2,1,2,1,2,1,2,
%T 1,9,1,2,1,4,1,2,1,2,3,2,1,2,1,2,1,2,1,6,1,4,1,2,1,12,1,2,3,1,1,2,1,2,
%U 1,2,1,18,1,2,3,2,1,2,1,10,1,2,1,12,1,2,1,4,1,6,1,2,1,2,1,4,1,2,3,1,1,2,1,4,1
%N a(n) = gcd(n, A293442(n)).
%H Antti Karttunen, <a href="/A331310/b331310.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = gcd(n, A293442(n)).
%F A331310(n) = A331287(n) / A331311(n).
%o (PARI)
%o A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A293442(n) = factorback(apply(e -> A019565(e),factor(n)[,2]));
%o A331310(n) = gcd(n, A293442(n));
%Y Cf. A019565, A293442, A331287, A331311.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 20 2020