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A191645 Numerators of the n-th partial "harmonic" sum of 1 + inverse semiprimes. 1

%I

%S 5,17,55,293,2141,445,457,5153,131597,1745411,1772711,30586537,

%T 31024117,597115873,604577173,14050770329,99311504603,100230122303,

%U 101081931443,101903852543

%N Numerators of the n-th partial "harmonic" sum of 1 + inverse semiprimes.

%C 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 This is the semiprime analog of A024528.

%e a(1) = 5 because 1 + 1/4 = 5/4.

%e a(2) = 17 because 1 + 1/4 + 1/6 = 17/12.

%e a(3) = 55 because 1 + 1/4 + 1/6 + 1/9 = 55/36.

%p A191645 := proc(n) 1+add(1/A001358(i),i=1..n) ; numer(%) ; end proc:

%p seq(A191645(n),n=1..20) ; # _R. J. Mathar_, Jun 16 2011

%t With[{sp=Join[{1},Select[Range[100],PrimeOmega[#]==2&]]},Rest[ Numerator[ Accumulate[1/sp]]]] (* _Harvey P. Dale_, May 01 2015 *)

%o (PARI) s=1; for(k=1,99, bigomega(k)==2 & print1(numerator(s+=1/k)", ")) \\ _M. F. Hasler_, Jun 17 2011

%Y Cf. A001358, A112141, A001008, A140123, A024528.

%K nonn,easy,frac

%O 1,1

%A _Jonathan Vos Post_, Jun 09 2011

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Last modified February 23 13:14 EST 2020. Contains 332159 sequences. (Running on oeis4.)