%I A140122
%S A140122 1,1,7,17,209,25,37,281,9797,92711,120011,1589737,2027317,30861373,
%T A140122 38322673,735926129,6107595203,5188977503,6040786643,5218865543,
%U A140122 174771852097,4738609625857,5386574286277,4776172794577,197777244862999
%N A140122 Negative of numerator of Sum_{k=1..n} (-1)^k / semiprime(k).
%e A140122 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.
%p A140122 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 (mathar(AT)strw.leidenuniv.nl), 
               May 13 2008
%Y A140122 Cf. A001358, A002110, A024530, A140123.
%Y A140122 Sequence in context: A118108 A147643 A061159 this_sequence A092240 A110120 
               A053584
%Y A140122 Adjacent sequences: A140119 A140120 A140121 this_sequence A140123 A140124 
               A140125
%K A140122 easy,frac,nonn
%O A140122 1,3
%A A140122 Jonathan Vos Post (jvospost3(AT)gmail.com), May 09 2008
%E A140122 Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               May 13 2008