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A356168 Greatest common divisor of n and A003961(A356164(n)), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).

%I A356168 #10 Jul 28 2022 21:16:14
%S A356168 1,1,3,1,5,3,7,1,9,5,11,3,13,7,5,1,17,9,19,5,21,11,23,3,25,13,27,7,29,
%T A356168 15,31,1,33,17,7,9,37,19,39,5,41,21,43,11,15,23,47,3,49,25,51,13,53,
%U A356168 27,55,7,57,29,59,15,61,31,63,1,65,33,67,17,69,7,71,9,73,37,25,19,11,39,79,5,81,41,83,21,85,43
%N A356168 Greatest common divisor of n and A003961(A356164(n)), where A356164(n) is the smallest positive k such that n divides k*A003961(k), and A003961 is fully multiplicative with a(p) = nextprime(p).
%H A356168 Antti Karttunen, <a href="/A356168/b356168.txt">Table of n, a(n) for n = 1..65537</a>
%H A356168 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A356168 a(n) = gcd(n, A003961(A356164(n))).
%F A356168 a(n) = gcd(n, A356169(n)) = n - A356169(n).
%o A356168 (PARI)
%o A356168 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A356168 A356168(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(gcd(n,A003961(k)))));
%Y A356168 Cf. A003961, A356164, A356166, A356167, A356169.
%K A356168 nonn
%O A356168 1,3
%A A356168 _Antti Karttunen_, Jul 28 2022