A185279 -id:A185279 - cp's OEIS frontend

A197629 Number of ways to write n as the sum of two coprime, squarefree, composite, positive integers.

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, 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, 2, 0, 3, 0, 4, 1, 0, 1, 3, 0, 5, 0, 2, 0, 4, 0, 1, 2

Offset: 1

Jason Holland, Oct 16 2011

nonn

			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).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A185279.

function [asubn]=ccsf(n)
% ccsf(n) returns the n-th term of the sequence of composite, coprime, square
% free sums of the integer n
r=0;
k=6;
while k0
r = r+1;
end
end
end
k=k+1;
end
asubn=r;
end

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

A232721 Numbers not representable as the sum of two coprime nonprime numbers.

Original entry on oeis.org

1, 3, 4, 6, 8, 12, 14, 18, 20, 24, 30, 32, 38, 42, 48, 54, 60, 72, 80, 84, 90, 108, 110, 132, 138, 140, 150, 180

Offset: 1

Irina Gerasimova, Nov 28 2013

Numbers n such that A185279(n) = 0. 1 and 3 together with A141096.

Cf. A062303, A018252, A141095, A141098.

t = Table[Length[Select[Range[n/2], ! PrimeQ[#] && ! PrimeQ[n - #] && GCD[#, n - #] == 1 &]], {n, 2000}]; Flatten[Position[t, 0]] (* T. D. Noe, Dec 05 2013 *)

cp's OEIS Frontend

A197629 Number of ways to write n as the sum of two coprime, squarefree, composite, positive integers.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

MATLAB

PARI