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A364255 a(n) = gcd(n, A163511(n)).

%I A364255 #21 Sep 01 2023 15:23:26
%S A364255 1,1,2,3,4,1,6,1,8,9,2,1,12,1,2,1,16,1,18,1,4,3,2,1,24,5,2,1,4,1,2,1,
%T A364255 32,3,2,5,36,1,2,1,8,1,6,1,4,3,2,1,48,1,10,1,4,1,2,11,8,3,2,1,4,1,2,1,
%U A364255 64,1,6,1,4,3,10,1,72,1,2,5,4,7,2,1,16,27,2,1,12,5,2,1,8,1,6,1,4,3,2,1,96,1,2,1,20,1,2,1,8,105
%N A364255 a(n) = gcd(n, A163511(n)).
%H A364255 Antti Karttunen, <a href="/A364255/b364255.txt">Table of n, a(n) for n = 0..16383</a>
%H A364255 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A364255 From _Antti Karttunen_, Sep 01 2023: (Start)
%F A364255 a(n) = gcd(n, A364258(n)) = gcd(A163511(n), A364258(n)).
%F A364255 a(n) = n / A364491(n) = A163511(n)/ A364492(n).
%F A364255 (End)
%o A364255 (Python)
%o A364255 from math import gcd
%o A364255 from sympy import nextprime
%o A364255 def A364255(n):
%o A364255     c, p, k = 1, 1, n
%o A364255     while k:
%o A364255         c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
%o A364255         k >>= s+1
%o A364255     return gcd(c*p,n) # _Chai Wah Wu_, Jul 25 2023
%o A364255 (PARI)
%o A364255 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 A364255 A364255(n) = gcd(n, A163511(n)); \\ _Antti Karttunen_, Sep 01 2023
%Y A364255 Cf. A163511, A364257 (Dirichlet inverse), A364258, A364491, A364492, A364493.
%Y A364255 Cf. also A364254, A364256, A339969, A364500, A364949.
%K A364255 nonn
%O A364255 0,3
%A A364255 _Antti Karttunen_, Jul 16 2023