A088183 Number of ways to write n as a sum of two coprime semiprimes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 4, 1, 0, 1, 4, 0, 2, 0, 1, 0, 3, 0, 4, 0, 1, 2, 5, 0, 6, 0, 1, 3, 1, 0, 4, 1, 3, 0, 6, 0, 5, 3, 1, 2, 3, 0, 5, 0, 3, 2, 7, 0, 1, 3, 4, 1, 4, 0, 6, 2, 2, 3, 6, 0, 7, 1, 4, 2, 6, 1

Offset: 1

Author

Reinhard Zumkeller, Sep 22 2003

Keywords

• nonn

Comments

a(A088184(n))>0, a(A088185(n))=0.

Is a(n)>0 for n>210? see conjecture in A072931.

The graph of this sequence is compelling evidence that 210 is the last term of sequence A088185. - T. D. Noe, Apr 10 2007

Examples

			a(64)=3: 64 = 3*3+5*11 = 3*5+7*7 = 5*5+3*13, (A072931(64)=5).
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• Eric Weisstein's World of Mathematics, Semiprime
• Eric Weisstein's World of Mathematics, Relatively Prime

Crossrefs

Cf. A072931, A001358.

Programs

Mathematica

cpspQ[{a_,b_}]:=PrimeOmega[a]==PrimeOmega[b]==2&&CoprimeQ[a,b]; Table[ Count[ IntegerPartitions[n,{2}],?(cpspQ[#]&)],{n,110}] (* _Harvey P. Dale, Sep 10 2019 *)

PARI

a(n)=sum(i=1, n, sum(j=1, i, if (gcd(i,j)==1, if (abs(bigomega(i)-2) +abs(bigomega(j)-2) +abs(n-i-j),0,1)))) \\ after A072966; Michel Marcus, Sep 08 2015