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 A191645 Numerators of the n-th partial "harmonic" sum of 1 + inverse semiprimes. 1
 5, 17, 55, 293, 2141, 445, 457, 5153, 131597, 1745411, 1772711, 30586537, 31024117, 597115873, 604577173, 14050770329, 99311504603, 100230122303, 101081931443, 101903852543 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, ... This is the semiprime analog of A024528. LINKS EXAMPLE a(1) =  5 because 1 + 1/4 = 5/4. a(2) = 17 because 1 + 1/4 + 1/6 = 17/12. a(3) = 55 because 1 + 1/4 + 1/6 + 1/9 = 55/36. MAPLE A191645 := proc(n) 1+add(1/A001358(i), i=1..n) ; numer(%) ; end proc: seq(A191645(n), n=1..20) ; # R. J. Mathar, Jun 16 2011 MATHEMATICA With[{sp=Join[{1}, Select[Range[100], PrimeOmega[#]==2&]]}, Rest[ Numerator[ Accumulate[1/sp]]]] (* Harvey P. Dale, May 01 2015 *) PROG (PARI) s=1; for(k=1, 99, bigomega(k)==2 & print1(numerator(s+=1/k)", "))  \\ M. F. Hasler, Jun 17 2011 CROSSREFS Cf. A001358, A112141, A001008, A140123, A024528. Sequence in context: A183712 A244235 A081495 * A146240 A112410 A146271 Adjacent sequences:  A191642 A191643 A191644 * A191646 A191647 A191648 KEYWORD nonn,easy,frac AUTHOR Jonathan Vos Post, Jun 09 2011 STATUS approved

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Last modified January 21 11:11 EST 2020. Contains 331105 sequences. (Running on oeis4.)