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A356169 a(n) = n - gcd(n, 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 A356169 #10 Jul 28 2022 21:16:18
%S A356169 0,1,0,3,0,3,0,7,0,5,0,9,0,7,10,15,0,9,0,15,0,11,0,21,0,13,0,21,0,15,
%T A356169 0,31,0,17,28,27,0,19,0,35,0,21,0,33,30,23,0,45,0,25,0,39,0,27,0,49,0,
%U A356169 29,0,45,0,31,0,63,0,33,0,51,0,63,0,63,0,37,50,57,66,39,0,75,0,41,0,63,0,43,0,77,0,75,0,69
%N A356169 a(n) = n - gcd(n, 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 A356169 Antti Karttunen, <a href="/A356169/b356169.txt">Table of n, a(n) for n = 1..65537</a>
%H A356169 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A356169 a(n) = n - A356168(n) = n - gcd(n, A003961(A356164(n))).
%o A356169 (PARI)
%o A356169 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A356169 A356169(n) = for(k=1, oo, if((k*A003961(k))%n==0, return(n-gcd(n,A003961(k)))));
%Y A356169 Cf. A003961, A356164, A356166, A356168, A356171 (positions of 0's), A356172.
%K A356169 nonn
%O A356169 1,4
%A A356169 _Antti Karttunen_, Jul 28 2022