A325809 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.

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

Offset: 1

Author

Antti Karttunen, May 25 2019

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1158

Crossrefs

Cf. A228058, A325807, A325819.

Programs

PARI

up_to = 25000;
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));
A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(kA228058(n), k++; v[k] = n)); (v); };
v228058 = A228058list(up_to);
A228058(n) = v228058[n];
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))); };
sumbybits(v,b) = { my(s=0,i=1); while(b>0,s += (b%2)*v[i]; i++; b >>= 1); (s); };
A325809(n) = A325807(A228058(n));

Formula

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