A133795 a(n) = n-th semiprime + n-th non-semiprime.

5, 8, 12, 15, 21, 23, 32, 34, 38, 42, 50, 52, 54, 58, 62, 70, 76, 79, 84, 87, 89, 94, 101, 106, 114, 118, 124, 128, 130, 132, 138, 141, 144, 147, 159, 165, 171, 177, 179, 182, 185, 187, 195, 200, 202, 211, 213, 215, 218, 221, 231, 236, 238, 241, 247, 252, 261

Offset: 1

Author

Jonathan Vos Post, Jan 05 2008

Keywords

• easy
• nonn
• less

Comments

Semiprime analog of A022797 n-th prime + n-th nonprime. a(n) is prime for n = 1, 6, 18, 21, 23. a(n) is itself semiprime for n = 4, 5, 22, 25, 38, 39, 57, 62, 69, 77 of which first 10 indices all but n=5 are themselves semiprimes.

Examples

			a(1) = 1st semiprime + 1st nonsemiprime = 4 + 1 = 5.
a(2) = 2nd semiprime + 2nd nonsemiprime = 6 + 2 = 8.
a(3) = 3rd semiprime + 3rd nonsemiprime = 9 + 3 = 12.
		

Crossrefs

Cf. A000040, A001358, A022797, A100959.

Programs

Maple

A100959 := proc(n) option remember; local a ; if n = 1 then 1 ; else for a from A100959(n-1)+1 do if numtheory[bigomega](a) <> 2 then RETURN(a) ; fi ; od: fi ; end: A001358 := proc(n) option remember ; local a ; if n = 1 then 4 ; else for a from A001358(n-1)+1 do if numtheory[bigomega](a) = 2 then RETURN(a) ; fi ; od: fi ; end: A133795 := proc(n) A100959(n)+A001358(n) ; end: seq(A133795(n),n=1..100) ; # R. J. Mathar, Jan 09 2008

Mathematica

Module[{nn=200,spr,non},spr=Select[Range[nn],PrimeOmega[#]==2&];non=Take[ Complement[ Range[ nn],spr],Length[ spr]];Total/@Thread[{spr,non}]] (* Harvey P. Dale, Sep 06 2024 *)

Formula

a(n) = A001358(n) + A100959(n).

Extensions

Corrected and extended by R. J. Mathar, Jan 09 2008