A197629 - OEIS

%I #15 Apr 25 2016 12:05:03

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,

%T 0,0,1,0,0,0,2,0,2,0,0,0,2,0,2,0,0,0,2,0,1,0,1,0,2,0,5,0,0,0,1,0,3,1,

%U 2,0,3,0,4,1,0,1,3,0,5,0,2,0,4,0,1,2

%N Number of ways to write n as the sum of two coprime, squarefree, composite, positive integers.

%H Charles R Greathouse IV, <a href="/A197629/b197629.txt">Table of n, a(n) for n = 1..10000</a>

%e a(29) is the first nonzero term since 29=15+14. The first nonzero even term is a(68) since 68=3(11)+5(7). Then the first even term with a value greater than one is a(86) since 86=3(7)+5(13) and 86=5(7)+3(17).

%o (MATLAB)

%o function [asubn]=ccsf(n)

%o % ccsf(n) returns the n-th term of the sequence of composite, coprime, square

%o % free sums of the integer n

%o r=0;

%o k=6;

%o while k<n/2,

%o if isprime(k)+isprime(n-k) == 0

%o if gcd(k,n-k) == 1

%o if prod(diff(factor(k)))*prod(diff(factor(n-k)))>0

%o r = r+1;

%o end

%o end

%o end

%o k=k+1;

%o end

%o asubn=r;

%o end

%o (PARI) a(n)=sum(k=4,(n-1)\2,gcd(k,n-k)==1&&!isprime(k)&&!isprime(n-k)&&issquarefree(k)&&issquarefree(n-k)) \\ _Charles R Greathouse IV_, Oct 18 2011

%Y Cf. A185279.

%K nonn

%O 1,41

%A _Jason Holland_, Oct 16 2011