A325826 - OEIS

%I #15 Jun 02 2019 23:42:44

%S 0,1,1,3,1,1,1,7,4,7,1,15,1,9,7,15,1,20,1,21,11,13,1,35,6,13,13,1,1,

%T 41,1,31,13,19,13,55,1,21,17,49,1,53,1,39,31,23,1,75,8,43,19,43,1,65,

%U 17,63,23,31,1,107,1,33,41,63,19,77,1,57,25,73,1,122,1,39,49,61,19,89,1,105,40,43,1,139,23,43,31,91,1,143,19,75

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

%H Antti Karttunen, <a href="/A325826/b325826.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A325826/a325826.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A325818(n) - n = A001065(n) - A325817(n) = A325976(n) - A033879(n).

%F a(A000040(n)) = a(A000396(n)) = 1.

%F a(n) >= A325969(n).

%F gcd(a(n), A325976(n)) = 1.

%o (PARI) A325826(n) = { my(s=sigma(n)); forstep(k=s-n, 0, -1, if(1==gcd((n+n-sigma(n)), k), return(k))); };

%o (PARI)

%o A325818(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(s-i))); };

%o A325826(n) = (A325818(n) - n);

%Y Cf. A000040, A000203, A000396, A001065, A033879, A324213, A325817, A325818, A325969, A325970, A325976.

%K nonn

%O 1,4

%A _Antti Karttunen_, May 29 2019