A191645 - OEIS

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A191645

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

5, 17, 55, 293, 2141, 445, 457, 5153, 131597, 1745411, 1772711, 30586537, 31024117, 597115873, 604577173, 14050770329, 99311504603, 100230122303, 101081931443, 101903852543

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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

Table of n, a(n) for n=1..20.

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 *)