This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191645 #19 Feb 21 2019 13:50:53
%S A191645 5,17,55,293,2141,445,457,5153,131597,1745411,1772711,30586537,
%T A191645 31024117,597115873,604577173,14050770329,99311504603,100230122303,
%U A191645 101081931443,101903852543
%N A191645 Numerators of the n-th partial "harmonic" sum of 1 + inverse semiprimes.
%C A191645 Denominators appear to be the same as A140123. The fractions begin: 5/4, 17/12, 55/36, 293/180, 2141/1260, 445/252, 457/252, 5153/2772, 131597/69300, ...
%C A191645 This is the semiprime analog of A024528.
%e A191645 a(1) = 5 because 1 + 1/4 = 5/4.
%e A191645 a(2) = 17 because 1 + 1/4 + 1/6 = 17/12.
%e A191645 a(3) = 55 because 1 + 1/4 + 1/6 + 1/9 = 55/36.
%p A191645 A191645 := proc(n) 1+add(1/A001358(i),i=1..n) ; numer(%) ; end proc:
%p A191645 seq(A191645(n),n=1..20) ; # _R. J. Mathar_, Jun 16 2011
%t A191645 With[{sp=Join[{1},Select[Range[100],PrimeOmega[#]==2&]]},Rest[ Numerator[ Accumulate[1/sp]]]] (* _Harvey P. Dale_, May 01 2015 *)
%o A191645 (PARI) s=1; for(k=1,99, bigomega(k)==2 & print1(numerator(s+=1/k)", ")) \\ _M. F. Hasler_, Jun 17 2011
%Y A191645 Cf. A001358, A112141, A001008, A140123, A024528.
%K A191645 nonn,easy,frac
%O A191645 1,1
%A A191645 _Jonathan Vos Post_, Jun 09 2011