Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Oct 03 2015 23:27:13
%S 4,12,36,180,1260,252,252,2772,69300,900900,900900,15315300,15315300,
%T 290990700,290990700,6692786100,46849502700,46849502700,46849502700,
%U 46849502700,1358635578300,42117702927300,42117702927300,42117702927300
%N Denominator of Sum_{k=1..n} (-1)^k / semiprime(k).
%e The first 10 values of A140122(n)/a(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) = 900900. 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) = 46849502700.
%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: A140123 := proc(n) local k ; denom(add ( (-1)^k/A001358(k),k=1..n)) ; end: seq(A140123(n),n=1..30) ; # _R. J. Mathar_, May 13 2008
%Y Cf. A001358, A002110, A024530, A140122.
%K easy,frac,nonn
%O 1,1
%A _Jonathan Vos Post_, May 09 2008
%E More terms from _R. J. Mathar_, May 13 2008