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A176504 a(n) = m + k where prime(m)*prime(k) = semiprime(n). 30
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, 12, 10, 13, 16, 11, 17, 14, 12, 18, 11, 10, 19, 15, 16, 12, 20, 17, 21, 11, 13, 22, 14, 23, 18, 13, 24, 12, 19, 25, 20, 15, 12, 26, 21, 27, 14, 16, 28, 13, 22, 29, 17, 15, 30, 23, 13, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = A056239(A001358(n)) = A338912(n) + A338913(n). - Gus Wiseman, Dec 04 2020
EXAMPLE
From Gus Wiseman, Dec 04 2020: (Start)
A semiprime (A001358) is a product of any two prime numbers. The sequence of all semiprimes together with their prime indices and weights begins:
4: 1 + 1 = 2
6: 1 + 2 = 3
9: 2 + 2 = 4
10: 1 + 3 = 4
14: 1 + 4 = 5
15: 2 + 3 = 5
21: 2 + 4 = 6
22: 1 + 5 = 6
25: 3 + 3 = 6
26: 1 + 6 = 7
(End)
MAPLE
From R. J. Mathar, Apr 20 2010: (Start)
isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
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:
A084126 := proc(n) min(op(numtheory[factorset](A001358(n)))) ; end proc:
A084127 := proc(n) max(op(numtheory[factorset](A001358(n)))) ; end proc:
A176504 := proc(n) numtheory[pi](A084126(n)) + numtheory[pi](A084127(n)) ; end proc: seq(A176504(n), n=1..80) ; (End)
MATHEMATICA
Table[If[SquareFreeQ[n], Total[PrimePi/@First/@FactorInteger[n]], 2*PrimePi[Sqrt[n]]], {n, Select[Range[100], PrimeOmega[#]==2&]}] (* Gus Wiseman, Dec 04 2020 *)
CROSSREFS
A056239 is the version for not just semiprimes.
A087794 gives the product of the same two indices.
A176506 gives the difference of the same two indices.
A338904 puts the n-th semiprime in row a(n).
A001358 lists semiprimes.
A006881 lists squarefree semiprimes.
A338898/A338912/A338913 give the prime indices of semiprimes.
A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with product/sum/difference A339361/A339362/A338900.
Sequence in context: A027434 A319434 A174697 * A196162 A071940 A085883
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entries checked by R. J. Mathar, Apr 20 2010
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)