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A325976 a(n) is the largest k <= n such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.

%I A325976 #11 Jun 02 2019 23:43:21
%S A325976 1,2,3,4,5,1,7,8,9,9,11,11,13,13,13,16,17,17,19,19,21,21,23,23,25,23,
%T A325976 27,1,29,29,31,32,31,33,35,36,37,37,39,39,41,41,43,43,43,43,47,47,49,
%U A325976 50,49,49,53,53,55,55,57,57,59,59,61,61,63,64,65,65,67,67,67,69,71,71,73,73,75,73,77,77,79,79,81,81,83,83,85,83
%N A325976 a(n) is the largest k <= n such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.
%H A325976 Antti Karttunen, <a href="/A325976/b325976.txt">Table of n, a(n) for n = 1..16385</a>
%H A325976 Antti Karttunen, <a href="/A325976/a325976.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A325976 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A325976 a(n) = n - A325817(n) = A033879(n) + A325826(n).
%F A325976 a(n) >= A325959(n).
%F A325976 gcd(a(n), A325826(n)) = 1.
%o A325976 (PARI) A325976(n) = { my(s=sigma(n)); forstep(k=n, 0, -1, if(1==gcd((n+n-s), k), return(k))); };
%o A325976 (PARI)
%o A325976 A325817(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(i))); };
%o A325976 A325976(n) = (n - A325817(n));
%Y A325976 Cf. A033879, A325817, A325818, A325826, A325959.
%K A325976 nonn
%O A325976 1,2
%A A325976 _Antti Karttunen_, Jun 01 2019