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A325961 a(n) is the least k >= A061228(n)-1 such that n-k and n-(sigma(n)-k) are relatively prime, or 0 if no such k <= sigma(n) exists.

%I A325961 #17 Jun 02 2019 00:51:40
%S A325961 1,3,0,5,0,7,0,9,11,11,0,13,0,15,20,17,0,19,0,21,24,23,0,25,29,27,30,
%T A325961 29,0,31,0,33,38,35,40,37,0,39,42,41,0,43,0,45,50,47,0,49,55,51,58,53,
%U A325961 0,55,60,57,60,59,0,61,0,63,66,65,70,67,0,69,74,71,0,73,0,75,78,77,84,79,0,81,83,83,0,85,90,87,92,89,0,91,100
%N A325961 a(n) is the least k >= A061228(n)-1 such that n-k and n-(sigma(n)-k) are relatively prime, or 0 if no such k <= sigma(n) exists.
%C A325961 a(n) attains the value of A325818(n) only with n = 1, 2 and the even terms of A000396. Note that A000203(n) > ((n+A020639(n))-1) with composite n.
%H A325961 Antti Karttunen, <a href="/A325961/b325961.txt">Table of n, a(n) for n = 1..16384</a>
%H A325961 Antti Karttunen, <a href="/A325961/a325961.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A325961 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A325961 a(n) = 0 if and only if n is either an odd prime or an odd perfect number, but if n is neither, then a(n) = 2n - A325962(n).
%o A325961 (PARI)
%o A325961 A020639(n) = if(1==n, n, factor(n)[1, 1]);
%o A325961 A325961(n) = { my(s=sigma(n)); for(i=(-1)+n+A020639(n), s, if(1==gcd(n-i, n-(s-i)), return(i))); (0); };
%Y A325961 Cf. A000203, A000396, A020639, A061228, A324213, A325817, A325818, A325960, A325962, A325965, A325966.
%K A325961 nonn
%O A325961 1,2
%A A325961 _Antti Karttunen_, May 29 2019