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A374469 The odd part of gcd(n, A163511(n)).

%I A374469 #11 Aug 07 2024 15:11:26
%S A374469 1,1,1,3,1,1,3,1,1,9,1,1,3,1,1,1,1,1,9,1,1,3,1,1,3,5,1,1,1,1,1,1,1,3,
%T A374469 1,5,9,1,1,1,1,1,3,1,1,3,1,1,3,1,5,1,1,1,1,11,1,3,1,1,1,1,1,1,1,1,3,1,
%U A374469 1,3,5,1,9,1,1,5,1,7,1,1,1,27,1,1,3,5,1,1,1,1,3,1,1,3,1,1,3,1,1,1,5,1,1,1,1,105
%N A374469 The odd part of gcd(n, A163511(n)).
%H A374469 Antti Karttunen, <a href="/A374469/b374469.txt">Table of n, a(n) for n = 0..100000</a>
%F A374469 a(n) = A000265(A364255(n)) = A000265(gcd(n, A163511(n))).
%F A374469 For n >= 1, a(n) = A364255(n) / A006519(n).
%F A374469 For n >= 0, a(2*n) = a(n).
%o A374469 (PARI)
%o A374469 A000265(n) = (n>>valuation(n,2));
%o A374469 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A374469 A364255(n) = gcd(n, A163511(n));
%o A374469 A374469(n) = A000265(A364255(n));
%Y A374469 Cf. A000265, A006519, A007814, A163511, A364255, A364495 (fixed points).
%K A374469 nonn
%O A374469 0,4
%A A374469 _Antti Karttunen_, Aug 07 2024