cp's OEIS Frontend

A325969 a(n) = A325968(n) - n.

%I A325969 #12 Jun 02 2019 23:43:13
%S A325969 0,1,1,3,1,1,1,7,4,7,1,15,1,9,5,15,1,20,1,21,11,13,1,35,6,13,13,1,1,
%T A325969 41,1,31,11,19,13,55,1,21,17,49,1,53,1,39,29,23,1,75,8,43,17,43,1,65,
%U A325969 17,63,23,31,1,107,1,33,41,63,19,77,1,57,23,73,1,122,1,39,49,61,19,89,1,105,40,43,1,139,23,43,29,91,1,143,13,75,35,49
%N A325969 a(n) = A325968(n) - n.
%H A325969 Antti Karttunen, <a href="/A325969/b325969.txt">Table of n, a(n) for n = 1..16384</a>
%H A325969 Antti Karttunen, <a href="/A325969/a325969.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A325969 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A325969 a(n) = A325968(n) - n = A001065(n) - A325967(n).
%F A325969 a(n) = A325959(n) - A033879(n).
%F A325969 a(A000040(n)) = a(A000396(n)) = 1.
%F A325969 For all n, a(n) <= A325826(n).
%o A325969 (PARI)
%o A325969 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 A325969 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 A325969 A325969(n) = ((sigma(n)-n)-A325967(n));
%o A325969 (PARI)
%o A325969 A325968(n) = { my(divs=divisors(n), s=sigma(n),r,ms=0); for(b=0,(2^(length(divs)))-1,r=sumbybits(divs,b);if(1==gcd(n-(s-r),n-r),ms=max(r,ms))); (ms); };
%o A325969 sumbybits(v,b) = { my(s=0,i=1); while(b>0,s += (b%2)*v[i]; i++; b >>= 1); (s); };
%o A325969 A325969(n) = (A325968(n)-n);
%Y A325969 Cf. A000203, A009194, A033879, A325807, A325826, A325959, A325967, A325968.
%K A325969 nonn
%O A325969 1,4
%A A325969 _Antti Karttunen_, May 29 2019