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

1,1

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

Formula

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

Prog

(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(k<up_to, n++; if(isA228058(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));

Crossrefs

Cf. A228058, A325807, A325819.

Sequence in context: A160862 A152077 A215696 * A173461 A335160 A295782

Adjacent sequences: A325806 A325807 A325808 * A325810 A325811 A325812

Keyword

nonn

Author

Antti Karttunen, May 25 2019

Status

approved