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%I #5 Oct 03 2015 23:27:02
%S 1,1,7,17,209,25,37,281,9797,92711,120011,1589737,2027317,30861373,
%T 38322673,735926129,6107595203,5188977503,6040786643,5218865543,
%U 174771852097,4738609625857,5386574286277,4776172794577,197777244862999
%N Negative of numerator of Sum_{k=1..n} (-1)^k / semiprime(k).
%e 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 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
%Y Cf. A001358, A002110, A024530, A140123.
%K easy,frac,nonn
%O 1,3
%A _Jonathan Vos Post_, May 09 2008
%E Corrected and extended by _R. J. Mathar_, May 13 2008
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