A325809 - OEIS

%I #9 May 28 2019 19:34:49

%S 8,12,8,16,8,15,16,8,113,16,8,15,16,7,14,8,8,13,16,15,8,15,14,8,15,

%T 254,8,16,8,128,16,16,16,15,8,15,16,15,8,16,13,15,7,13,16,8,16,43008,

%U 8,8,126,8,15,15,15,8,16,8,14,8,15,16,8,16,60672,15,256,13,16,7,103,16,16,8,16,16,16,8,2015,16,8,15,16,39093,16

%N Let k = A228058(n). a(n) is the number of ways to partition the divisors of k into complementary subsets x and y so that the (k-Sum(x)) and (k-Sum(y)) are coprime.

%C The smallest value known so far occurs as a(449) = 6. A228058(449) = 23837 = 11^2 * 197.

%H Antti Karttunen, <a href="/A325809/b325809.txt">Table of n, a(n) for n = 1..1158</a>

%F a(n) = A325807(A228058(n)).

%o (PARI)

%o up_to = 25000;

%o isA228058(n) = if(!(n%2)||(omega(n)<2),0,my(f=factor(n),y=0); for(i=1,#f~,if(1==(f[i,2]%4), if((1==y)||(1!=(f[i,1]%4)),return(0),y=1), if(f[i,2]%2, return(0)))); (y));

%o A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };

%o v228058 = A228058list(up_to);

%o A228058(n) = v228058[n];

%o A325807(n) = { my(divs=divisors(n), s=sigma(n),r); sum(b=0,(2^(-1+length(divs)))-1,r=sumbybits(divs,2*b);(1==gcd(n-(s-r),n-r))); };

%o sumbybits(v,b) = { my(s=0,i=1); while(b>0,s += (b%2)*v[i]; i++; b >>= 1); (s); };

%o A325809(n) = A325807(A228058(n));

%Y Cf. A228058, A325807, A325819.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 25 2019