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A325959 a(n) = n - A325967(n).

%I A325959 #8 Jun 02 2019 23:42:52
%S A325959 1,2,3,4,5,1,7,8,9,9,11,11,13,13,11,16,17,17,19,19,21,21,23,23,25,23,
%T A325959 27,1,29,29,31,32,29,33,35,36,37,37,39,39,41,41,43,43,41,43,47,47,49,
%U A325959 50,47,49,53,53,55,55,57,57,59,59,61,61,63,64,65,65,67,67,65,69,71,71,73,73,75,73,77,77,79,79,81,81,83,83,85,83,83
%N A325959 a(n) = n - A325967(n).
%H A325959 Antti Karttunen, <a href="/A325959/b325959.txt">Table of n, a(n) for n = 1..25000</a>
%H A325959 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A325959 a(n) = n - A325967(n).
%F A325959 a(n) = A033879(n) + A325969(n).
%F A325959 For all n, a(n) <= A325976(n).
%o A325959 (PARI)
%o A325959 A325967aux(n, ds, s, ms, divs, from=1) = if(1==gcd((s-ds)-n,n-ds), return(ds), for(i=from, #divs, if(ds+divs[i] >= ms, return(ms), ms = min(ms,A325967aux(n, ds+divs[i], s, ms, divs, i+1)))); (ms));
%o A325959 A325967(n) = if(1==gcd(n, sigma(n)), 0, my(divs = List(divisors(n)), s=sigma(n), ms=2*s); fordiv(n,d, if(d>=ms, return(ms), listpop(divs,1); ms = min(ms,A325967aux(n, d, s, ms, divs)))); (ms));
%o A325959 A325959(n) = (n - A325967(n));
%Y A325959 Cf. A000203, A325967, A325968, A325969, A325976.
%K A325959 nonn
%O A325959 1,2
%A A325959 _Antti Karttunen_, Jun 01 2019