This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A176504 #13 Apr 18 2024 09:34:17
%S A176504 2,3,4,4,5,5,6,6,6,7,7,8,7,9,8,10,8,9,8,10,11,12,9,11,13,9,14,10,15,
%T A176504 12,10,13,16,11,17,14,12,18,11,10,19,15,16,12,20,17,21,11,13,22,14,23,
%U A176504 18,13,24,12,19,25,20,15,12,26,21,27,14,16,28,13,22,29,17,15,30,23,13,31
%N A176504 a(n) = m + k where prime(m)*prime(k) = semiprime(n).
%F A176504 a(n) = A056239(A001358(n)) = A338912(n) + A338913(n). - _Gus Wiseman_, Dec 04 2020
%F A176504 sqrt(n/(log n log log n)) << a(n) << n/log log n. - _Charles R Greathouse IV_, Apr 17 2024
%e A176504 From _Gus Wiseman_, Dec 04 2020: (Start)
%e A176504 A semiprime (A001358) is a product of any two prime numbers. The sequence of all semiprimes together with their prime indices and weights begins:
%e A176504 4: 1 + 1 = 2
%e A176504 6: 1 + 2 = 3
%e A176504 9: 2 + 2 = 4
%e A176504 10: 1 + 3 = 4
%e A176504 14: 1 + 4 = 5
%e A176504 15: 2 + 3 = 5
%e A176504 21: 2 + 4 = 6
%e A176504 22: 1 + 5 = 6
%e A176504 25: 3 + 3 = 6
%e A176504 26: 1 + 6 = 7
%e A176504 (End)
%p A176504 From _R. J. Mathar_, Apr 20 2010: (Start)
%p A176504 isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
%p A176504 A001358 := proc(n) option remember ; if n = 1 then return 4 ; else for a from procname(n-1)+1 do if isA001358(a) then return a; end if; end do; end if; end proc:
%p A176504 A084126 := proc(n) min(op(numtheory[factorset](A001358(n)))) ; end proc:
%p A176504 A084127 := proc(n) max(op(numtheory[factorset](A001358(n)))) ; end proc:
%p A176504 A176504 := proc(n) numtheory[pi](A084126(n)) + numtheory[pi](A084127(n)) ; end proc: seq(A176504(n),n=1..80) ; (End)
%t A176504 Table[If[SquareFreeQ[n],Total[PrimePi/@First/@FactorInteger[n]],2*PrimePi[Sqrt[n]]],{n,Select[Range[100],PrimeOmega[#]==2&]}] (* _Gus Wiseman_, Dec 04 2020 *)
%Y A176504 A056239 is the version for not just semiprimes.
%Y A176504 A087794 gives the product of the same two indices.
%Y A176504 A176506 gives the difference of the same two indices.
%Y A176504 A338904 puts the n-th semiprime in row a(n).
%Y A176504 A001358 lists semiprimes.
%Y A176504 A006881 lists squarefree semiprimes.
%Y A176504 A338898/A338912/A338913 give the prime indices of semiprimes.
%Y A176504 A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with product/sum/difference A339361/A339362/A338900.
%Y A176504 Cf. A001222, A046315, A065516, A084126, A084127, A100484, A112798, A115392, A128301, A338906/A338907.
%K A176504 nonn
%O A176504 1,1
%A A176504 _Juri-Stepan Gerasimov_, Apr 19 2010
%E A176504 Entries checked by _R. J. Mathar_, Apr 20 2010