cp's OEIS Frontend

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

%I A088183 #13 Feb 16 2025 08:32:51
%S A088183 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,
%T A088183 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,
%U A088183 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
%N A088183 Number of ways to write n as a sum of two coprime semiprimes.
%C A088183 a(A088184(n))>0, a(A088185(n))=0.
%C A088183 Is a(n)>0 for n>210? see conjecture in A072931.
%C A088183 The graph of this sequence is compelling evidence that 210 is the last term of sequence A088185. - _T. D. Noe_, Apr 10 2007
%H A088183 T. D. Noe, <a href="/A088183/b088183.txt">Table of n, a(n) for n=1..10000</a>
%H A088183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%H A088183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RelativelyPrime.html">Relatively Prime</a>
%e A088183 a(64)=3: 64 = 3*3+5*11 = 3*5+7*7 = 5*5+3*13, (A072931(64)=5).
%t A088183 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 *)
%o A088183 (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
%Y A088183 Cf. A072931, A001358.
%K A088183 nonn
%O A088183 1,19
%A A088183 _Reinhard Zumkeller_, Sep 22 2003