A140122 Negative of numerator of Sum_{k=1..n} (-1)^k / semiprime(k).

1, 1, 7, 17, 209, 25, 37, 281, 9797, 92711, 120011, 1589737, 2027317, 30861373, 38322673, 735926129, 6107595203, 5188977503, 6040786643, 5218865543, 174771852097, 4738609625857, 5386574286277, 4776172794577, 197777244862999

Offset: 1

Author

Jonathan Vos Post, May 09 2008

Keywords

• easy
• frac
• nonn

Examples

			The first 10 values of a(n)/A140123(n) = -1/4, -1/12, -7/36, -17/180, -209/1260, -25/252, -37/252, -281/2772, -9797/69300, -92711/900900. The 10th term of the sum is (-1/4)+(1/6)-(1/9)+(1/10)-(1/14)+(1/15)-(1/21)+(1/22)-(1/25)+(1/26) = -92711/900900 hence a(10) = -(-92711) = 92711. The 20th term of the alternating sum is (-1/4)+(1/6)-(1/9)+(1/10)-(1/14)+(1/15)-(1/21)+(1/22)-(1/25)+(1/26)-(1/33)+(1/34)-(1/35)+(1/38)-(1/39)+(1/46)-(1/49)+(1/51)-(1/55)+(1/57) = -5218865543/46849502700, hence a(20) = 5218865543.
		

Crossrefs

Cf. A001358, A002110, A024530, A140123.

Programs

Maple

A001358 := proc(n) 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: A140122 := proc(n) local k ; numer(-add ( (-1)^k/A001358(k),k=1..n)) ; end: seq(A140122(n),n=1..30) ; # R. J. Mathar, May 13 2008

Extensions

Corrected and extended by R. J. Mathar, May 13 2008