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A325971 a(n) is the least k >= A007947(n) such that -n + k and (n-sigma(n))+k are relatively prime.

%I A325971 #9 Jun 02 2019 00:52:19
%S A325971 1,2,4,2,6,7,8,2,3,11,12,7,14,15,16,2,18,7,20,11,22,23,24,7,5,27,4,27,
%T A325971 30,31,32,2,34,35,36,6,38,39,40,11,42,43,44,23,16,47,48,7,7,10,52,27,
%U A325971 54,7,56,15,58,59,60,31,62,63,22,2,66,67,68,35,70,71,72,7,74,75,16,39,78,79,80,11,3,83,84,43,86,87,88,23,90,31
%N A325971 a(n) is the least k >= A007947(n) such that -n + k and (n-sigma(n))+k are relatively prime.
%C A325971 a(n) is the least k >= A007947(n) such that n-k and n-(sigma(n)-k) are relatively prime.
%H A325971 Antti Karttunen, <a href="/A325971/b325971.txt">Table of n, a(n) for n = 1..20000</a>
%H A325971 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A325971 a(n) = A000203(n) - A325972(n).
%F A325971 a(n) = n - A325970(n).
%o A325971 (PARI)
%o A325971 A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
%o A325971 A325971(n) = { my(s=sigma(n)); for(i=A007947(n), s, if(1==gcd(n-i, n-(s-i)), return(i))); (0); };
%o A325971 A325971(n) = { my(s=sigma(n)); for(k=A007947(n), s, if(1==gcd(-n + k, (n-sigma(n))+k), return(k))); };
%Y A325971 Cf. A000203, A007947, A324213, A325817, A325961, A325965, A325970, A325972.
%K A325971 nonn
%O A325971 1,2
%A A325971 _Antti Karttunen_, May 31 2019