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A325818 a(n) is the largest k <= sigma(n) such that n-k and n-(sigma(n)-k) are relatively prime.

%I A325818 #14 Jun 02 2019 23:42:36
%S A325818 1,3,4,7,6,7,8,15,13,17,12,27,14,23,22,31,18,38,20,41,32,35,24,59,31,
%T A325818 39,40,29,30,71,32,63,46,53,48,91,38,59,56,89,42,95,44,83,76,69,48,
%U A325818 123,57,93,70,95,54,119,72,119,80,89,60,167,62,95,104,127,84,143,68,125,94,143,72,194,74,113,124,137,96
%N A325818 a(n) is the largest k <= sigma(n) such that n-k and n-(sigma(n)-k) are relatively prime.
%C A325818 a(n) is the largest k <= sigma(n) such that (-n + k) and (n-sigma(n))+k are coprime.
%H A325818 Antti Karttunen, <a href="/A325818/b325818.txt">Table of n, a(n) for n = 1..20000</a>
%H A325818 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A325818 a(n) = A000203(n) - A325817(n).
%F A325818 a(n) = n + A325826(n).
%F A325818 For all n:
%F A325818 a(A000396(n)) = A000396(n)+1.
%F A325818 a(n) >= A325961(n).
%F A325818 a(n) >= A325966(n).
%F A325818 a(n) >= A325968(n).
%o A325818 (PARI) A325818(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(s-i))); };
%Y A325818 Cf. A000203, A000396, A324213, A325817, A325826, A325961, A325966, A325968.
%K A325818 nonn
%O A325818 1,2
%A A325818 _Antti Karttunen_, May 29 2019