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A176504 a(n) = m + k where prime(m)*prime(k) = semiprime(n). 29
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

Table of n, a(n) for n=1..76.

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.

Cf. A001222, A046315, A065516, A084126, A084127, A100484, A112798, A115392, A128301, A338900, A338906/A338907.

Sequence in context: A027434 A319434 A174697 * A196162 A071940 A085883

Adjacent sequences:  A176501 A176502 A176503 * A176505 A176506 A176507

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Apr 19 2010

EXTENSIONS

Entries checked by R. J. Mathar, Apr 20 2010

STATUS

approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)