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%I #13 Apr 18 2024 09:34:17
%S 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 12,10,13,16,11,17,14,12,18,11,10,19,15,16,12,20,17,21,11,13,22,14,23,
%U 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 a(n) = m + k where prime(m)*prime(k) = semiprime(n).
%F a(n) = A056239(A001358(n)) = A338912(n) + A338913(n). - _Gus Wiseman_, Dec 04 2020
%F sqrt(n/(log n log log n)) << a(n) << n/log log n. - _Charles R Greathouse IV_, Apr 17 2024
%e From _Gus Wiseman_, Dec 04 2020: (Start)
%e 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 4: 1 + 1 = 2
%e 6: 1 + 2 = 3
%e 9: 2 + 2 = 4
%e 10: 1 + 3 = 4
%e 14: 1 + 4 = 5
%e 15: 2 + 3 = 5
%e 21: 2 + 4 = 6
%e 22: 1 + 5 = 6
%e 25: 3 + 3 = 6
%e 26: 1 + 6 = 7
%e (End)
%p From _R. J. Mathar_, Apr 20 2010: (Start)
%p isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
%p 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 A084126 := proc(n) min(op(numtheory[factorset](A001358(n)))) ; end proc:
%p A084127 := proc(n) max(op(numtheory[factorset](A001358(n)))) ; end proc:
%p A176504 := proc(n) numtheory[pi](A084126(n)) + numtheory[pi](A084127(n)) ; end proc: seq(A176504(n),n=1..80) ; (End)
%t 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 A056239 is the version for not just semiprimes.
%Y A087794 gives the product of the same two indices.
%Y A176506 gives the difference of the same two indices.
%Y A338904 puts the n-th semiprime in row a(n).
%Y A001358 lists semiprimes.
%Y A006881 lists squarefree semiprimes.
%Y A338898/A338912/A338913 give the prime indices of semiprimes.
%Y A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with product/sum/difference A339361/A339362/A338900.
%Y Cf. A001222, A046315, A065516, A084126, A084127, A100484, A112798, A115392, A128301, A338906/A338907.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Apr 19 2010
%E Entries checked by _R. J. Mathar_, Apr 20 2010
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